
import time
from collections import Counter
import matplotlib.pyplot as plt
import plotly.express as px
import statistics
import numpy as np
import pandas as pd
import seaborn as sns
from pandas_profiling import ProfileReport
from sklearn.model_selection import cross_val_score, train_test_split, GridSearchCV
from sklearn.feature_selection import SelectFromModel, SequentialFeatureSelector, VarianceThreshold
from sklearn.decomposition import PCA
from sklearn.linear_model import LinearRegression
from sklearn.ensemble import RandomForestRegressor, AdaBoostRegressor, GradientBoostingRegressor
from sklearn.tree import DecisionTreeRegressor
from sklearn.metrics import explained_variance_score
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import classification_report
from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay
from sklearn.metrics import f1_score

# config plot
pd.set_option('display.max_columns', None)
pd.set_option('display.expand_frame_repr', False)
pd.set_option('max_colwidth', None)

# random state value
random_state = 42

%matplotlib inline


dt = pd.read_csv("train.csv", sep=",")
df = pd.DataFrame(dt)
df


# generating profile report of the whole dataset - FIRST RUN ONLY
'''
profile = ProfileReport(df, title="PD_TPC2_Superconductors")
profile.to_file("appendix/PD_TPC2_Superconductors.html")
'''

'\nprofile = ProfileReport(df, title="PD_TPC2_Superconductors")\nprofile.to_file("appendix/PD_TPC2_Superconductors.html")\n'


# data types
df.dtypes

number_of_elements         int64
mean_atomic_mass         float64
wtd_mean_atomic_mass     float64
gmean_atomic_mass        float64
wtd_gmean_atomic_mass    float64
                          ...   
range_Valence              int64
wtd_range_Valence        float64
std_Valence              float64
wtd_std_Valence          float64
critical_temp            float64
Length: 82, dtype: object


# missing values
df.isnull().sum()

number_of_elements       0
mean_atomic_mass         0
wtd_mean_atomic_mass     0
gmean_atomic_mass        0
wtd_gmean_atomic_mass    0
                        ..
range_Valence            0
wtd_range_Valence        0
std_Valence              0
wtd_std_Valence          0
critical_temp            0
Length: 82, dtype: int64


# cheking for duplicates
Counter(df.duplicated())

Counter({False: 21197, True: 66})


# drop duplicates
df = df.drop_duplicates()


# cheking for duplicates
Counter(df.duplicated())

Counter({False: 21197})


# describe dataset
df.describe()


scalar = StandardScaler()
x = df.copy(deep=True)
column_names = []
for col in x.columns:
    column_names.append(col)

#Select numerical features
x = x[column_names].values

#Standardized values
x_standard = scalar.fit_transform(x)

standard_df = pd.DataFrame(x_standard, columns=column_names)

#Create dictionarie with the number of outliers for each feature
outliers = dict()
for i, val in enumerate(standard_df.columns):
    outliers[val] = dict()
    outliers[val]["count"] = len(np.where(abs(standard_df[val].values) > 3)[0])
    outliers[val]["propotion"] = outliers[val]["count"] / standard_df[val].shape[0]

outliers = pd.DataFrame(data=outliers).T
outliers.sort_values(by="count", ascending=False)


x_train = df.loc[:, df.columns != 'critical_temp']  # x_train set
x_train = pd.DataFrame(x_train, columns=x_train.columns)
x_train


y_train = df['critical_temp']  # y_train set
y_train = pd.DataFrame(y_train)
y_train


X_train, X_test, Y_train, Y_test = train_test_split(x_train, y_train, test_size=0.33, random_state=random_state)

X_train = pd.DataFrame(X_train, columns=X_train.columns)
X_test = pd.DataFrame(X_test, columns=X_test.columns)

Y_train = pd.DataFrame(Y_train)
Y_test = pd.DataFrame(Y_test)

print("Shapes:\n",
      "X_train: ", X_train.shape, "\n",
      "X_test: ", X_test.shape, "\n",
      "Y_train: ", Y_train.shape, "\n",
      "Y_test: ", Y_test.shape, "\n",
      )

Shapes:
 X_train:  (14201, 81) 
 X_test:  (6996, 81) 
 Y_train:  (14201, 1) 
 Y_test:  (6996, 1)


# Data Scaling 

scaler = StandardScaler()

x_train_scaled = pd.DataFrame(scaler.fit_transform(X_train), columns=x_train.columns)
x_test_scaled = pd.DataFrame(scaler.transform(X_test), columns=X_test.columns)


x_train_scaled


x_test_scaled


c = X_train.columns
variances = []
for c in X_train:
    var = np.var(np.log(df[c]))
    #var = np.var(X_train[c])
    d = {"Features": c, "Variance": var}
    variances.append(d)

var_log = pd.DataFrame(variances)

fig = px.bar(var_log, x='Features', y='Variance', width=1000, height=800)
fig.update_layout(xaxis=dict(tickfont=dict(size=5)))
fig.update_layout(yaxis_title="Log-Variance")
fig.show()

C:\Users\raimu\anaconda3\lib\site-packages\pandas\core\arraylike.py:364: RuntimeWarning: divide by zero encountered in log
  result = getattr(ufunc, method)(*inputs, **kwargs)


# function to test the explain variance score with linear regression, random forest regressor and decision tree regressor
def naif_model_testing(X_train, X_test, y_train, y_test):
    # test 3 approaches and print out the results

    rfr = RandomForestRegressor(n_estimators=100, random_state=random_state)
    rfr.fit(X_train, y_train)

    dtr = DecisionTreeRegressor(max_depth=5, random_state=random_state)
    dtr.fit(X_train, y_train)

    lmr = LinearRegression()
    lmr.fit(X_train, y_train)

    rf_preds = rfr.predict(X_test)
    dt_preds = dtr.predict(X_test)
    lr_preds = lmr.predict(X_test)

    print("RVE RFs: %7.4f" % explained_variance_score(y_test, rf_preds))
    print("RVE DTs: %7.4f" % explained_variance_score(y_test, dt_preds))
    print("RVE LRs: %7.4f" % explained_variance_score(y_test, lr_preds))


# function to select the best features with Select From Model algorithm for the regressors: Random Forest and Decision Tree
def sfm(x_train_scaled, Y_train, x_test_scaled, Y_test, estimator):
    N, M = x_train_scaled.shape

    est = estimator
    sel = SelectFromModel(estimator=est)
    sel.fit(x_train_scaled, Y_train.values.ravel())

    print("Threshold: ", sel.threshold_)

    features = sel.get_support()

    Features_selected = np.arange(M)[features]

    importances = sel.estimator_.feature_importances_
    features_index = sel.get_support(indices=True)

    importances_list = []
    features_name = []
    for i in features_index:
        importances_list.append(importances[i])
        features_name.append(x_train_scaled.columns[i])

    f_index_df = pd.DataFrame(Features_selected)
    fnames_df = pd.DataFrame(features_name)
    imp_df = pd.DataFrame(importances_list)

    imp_selected = pd.concat([f_index_df, fnames_df, imp_df], axis=1)
    imp_selected.columns = ["Index", "Selected Features", "Importance"]
    imp_selected_sort = imp_selected.sort_values(by="Importance", ascending=False)

    print("\nBest Selected Features with the respective Importance:\n")

    print(imp_selected_sort.to_string(index=False), "\n")

    print("\nExplained Variance Score:")
    nX_train = sel.transform(x_train_scaled)
    nX_test = sel.transform(x_test_scaled)
    naif_model_testing(nX_train, nX_test, Y_train.values.ravel(), Y_test.values.ravel())


# function to select the best features with Select From Model algorithm for Linear Regression classifier
def sfm_linear(x_train_scaled, Y_train, x_test_scaled, Y_test):
    N, M = x_train_scaled.shape

    est = LinearRegression()
    sel = SelectFromModel(estimator=est, threshold='1.25*mean')
    sel.fit(x_train_scaled, Y_train.values.ravel())

    print("Threshold: ", sel.threshold_)

    features = sel.get_support()

    Features_selected = np.arange(M)[features]

    coef = sel.estimator_.coef_
    features_index = sel.get_support(indices=True)

    coeficient_list = []
    features_name = []
    for i in features_index:
        coeficient_list.append(coef[i])
        features_name.append(x_train_scaled.columns[i])

    f_index_df = pd.DataFrame(Features_selected)
    fnames_df = pd.DataFrame(features_name)
    imp_df = pd.DataFrame(coeficient_list)

    imp_selected = pd.concat([f_index_df, fnames_df, imp_df], axis=1)
    imp_selected.columns = ["Index", "Selected Features", "Coeficient"]
    imp_selected_sort = imp_selected.sort_values(by="Coeficient", ascending=False)

    print("\nBest Selected Features with the respective Coeficient:\n")

    print(imp_selected_sort.to_string(index=False), "\n")

    print("\nExplained Variance Score:")
    nX_train = sel.transform(x_train_scaled)
    nX_test = sel.transform(x_test_scaled)
    naif_model_testing(nX_train, nX_test, Y_train.values.ravel(), Y_test.values.ravel())


# function to select the best features with Sequenctial Features Selector algorithm for Random Forest Regressor, Decision Tree Regressor and Linear Regression
def sfs(x_train_scaled, Y_train, x_test_scaled, Y_test, estimator):
    N, M = x_train_scaled.shape

    sfs = SequentialFeatureSelector(estimator, n_features_to_select=9)
    sfs.fit(x_train_scaled, Y_train.values.ravel())

    features = sfs.get_support()

    Features_selected = np.arange(M)[features]

    features_index = sfs.get_support(indices=True)

    features_name = []
    for i in features_index:
        features_name.append(x_train_scaled.columns[i])

    f_index_df = pd.DataFrame(Features_selected)
    fnames_df = pd.DataFrame(features_name)

    sfs_selected = pd.concat([f_index_df, fnames_df], axis=1)
    sfs_selected.columns = ["Index", "Selected Features"]

    print("\nBest Selected Features:\n")

    print(sfs_selected, "\n")

    print("\nExplained Variance Score:")
    nX_train = sfs.transform(x_train_scaled)
    nX_test = sfs.transform(x_test_scaled)
    naif_model_testing(nX_train, nX_test, Y_train.values.ravel(), Y_test.values.ravel())


# function to perform GridSearchCV
def best_model(x, y, estimator, params, cv):
    clf = GridSearchCV(estimator=estimator, param_grid=params, scoring='explained_variance', cv=cv, error_score='raise',
                       n_jobs=-1).fit(x, y)
    return {
        'Estimator': clf.best_estimator_,
        'Best Params': clf.best_params_,
        'Best Score': clf.best_score_,
        'Detailed Results': clf.cv_results_,
    }


# function to convert the dataframe with the final results of GridSearch to a CSV file
def result_to_file(algorithm_name, result_map, file_name):
    new_result = pd.DataFrame(result_map['Detailed Results'])
    new_result = new_result[['params', 'mean_test_score']]
    new_result = new_result.assign(Algorithm=algorithm_name)
    result = new_result[['Algorithm', 'params', 'mean_test_score']]
    result = pd.DataFrame(result)
    result.to_csv(file_name)
    return result


# correlation matrix
corr = df.corr(method='pearson')
fig = px.imshow(corr, text_auto=True, width=800, height=800)

fig.update_layout(
    yaxis=dict(tickfont=dict(size=5)),
    xaxis=dict(tickfont=dict(size=5)))

fig.show()


corr_target = pd.DataFrame(corr['critical_temp'])
corr_target = corr_target.drop(index="critical_temp")
corr_target.columns = ['critical_temp']

print("Features that are more correlated with target variable 'critical_temp':")
corr_target.loc[corr_target['critical_temp'] >= 0.5].sort_values(by='critical_temp', ascending=False)

Features that are more correlated with target variable 'critical_temp':


sfm(x_train_scaled, Y_train, x_test_scaled, Y_test, RandomForestRegressor(random_state=random_state))

Threshold:  0.012345679012345678

Best Selected Features with the respective Importance:

 Index               Selected Features  Importance
    67       range_ThermalConductivity    0.535776
    64   wtd_gmean_ThermalConductivity    0.122333
     9                 std_atomic_mass    0.029559
    74               wtd_gmean_Valence    0.022253
    66 wtd_entropy_ThermalConductivity    0.012598
    72                wtd_mean_Valence    0.012446 


Explained Variance Score:
RVE RFs:  0.9054
RVE DTs:  0.7628
RVE LRs:  0.5367


sfm(x_train_scaled, Y_train, x_test_scaled, Y_test, DecisionTreeRegressor(random_state=random_state))

Threshold:  0.012345679012345678

Best Selected Features with the respective Importance:

 Index             Selected Features  Importance
    67     range_ThermalConductivity    0.537984
    64 wtd_gmean_ThermalConductivity    0.122310
    74             wtd_gmean_Valence    0.039756
     9               std_atomic_mass    0.032484
    78             wtd_range_Valence    0.014258
    47        range_ElectronAffinity    0.014253
    10           wtd_std_atomic_mass    0.013537
    31                  mean_Density    0.013443
    62  wtd_mean_ThermalConductivity    0.012556 


Explained Variance Score:
RVE RFs:  0.9104
RVE DTs:  0.7687
RVE LRs:  0.6062


sfm_linear(x_train_scaled, Y_train, x_test_scaled, Y_test)

Threshold:  18.08131379095711

Best Selected Features with the respective Coeficient:

 Index            Selected Features  Coeficient
    22       wtd_mean_atomic_radius   86.176307
    72             wtd_mean_Valence   32.069839
    75              entropy_Valence   31.440442
    49         std_ElectronAffinity   28.530402
     1             mean_atomic_mass   27.228482
    14                wtd_gmean_fie   26.815100
     4        wtd_gmean_atomic_mass   25.051517
    62 wtd_mean_ThermalConductivity   23.832226
    25        entropy_atomic_radius   22.967635
    73                gmean_Valence   20.717748
    54         wtd_gmean_FusionHeat   19.613724
    17                    range_fie   19.120252
    26    wtd_entropy_atomic_radius   18.956435
    44   wtd_gmean_ElectronAffinity  -19.491360
    19                      std_fie  -20.478910
    47       range_ElectronAffinity  -23.460544
    76          wtd_entropy_Valence  -23.898121
    52          wtd_mean_FusionHeat  -26.328234
    12                 wtd_mean_fie  -28.595962
     2         wtd_mean_atomic_mass  -32.072898
    74            wtd_gmean_Valence  -36.704486
    15                  entropy_fie  -43.261368
    24      wtd_gmean_atomic_radius  -92.256168 


Explained Variance Score:
RVE RFs:  0.9176
RVE DTs:  0.7525
RVE LRs:  0.6497


#sfs(x_train_scaled, Y_train, x_test_scaled, Y_test, RandomForestRegressor(random_state= random_state))

sfsRF_out = open("appendix/sfs_RandomForest.txt", "r")
print(sfsRF_out.read())

Best Selected Features:

   Index           Selected Features
0      7           range_atomic_mass
1     10         wtd_std_atomic_mass
2     15                 entropy_fie
3     20                 wtd_std_fie
4     27         range_atomic_radius
5     38           wtd_range_Density
6     44  wtd_gmean_ElectronAffinity
7     61    mean_ThermalConductivity
8     72            wtd_mean_Valence 


Explained Variance Score:
RVE RFs:  0.9167
RVE DTs:  0.7385
RVE LRs:  0.5632


#sfs(x_train_scaled, Y_train, x_test_scaled, Y_test, DecisionTreeRegressor(random_state= random_state))

sfsDT_out = open("appendix/sfs_DecisionTree.txt", "r")
print(sfsDT_out.read())

Best Selected Features:

   Index              Selected Features
0      3              gmean_atomic_mass
1     25          entropy_atomic_radius
2     30          wtd_std_atomic_radius
3     37                  range_Density
4     44     wtd_gmean_ElectronAffinity
5     47         range_ElectronAffinity
6     49           std_ElectronAffinity
7     51                mean_FusionHeat
8     68  wtd_range_ThermalConductivity 


Explained Variance Score:
RVE RFs:  0.9109
RVE DTs:  0.7376
RVE LRs:  0.5445


#sfs(x_train_scaled, Y_train, x_test_scaled, Y_test, LinearRegression())

sfsLR_out = open("appendix/sfs_LinearRegression.txt", "r")
print(sfsLR_out.read())

Best Selected Features:

   Index                Selected Features
0     27              range_atomic_radius
1     42        wtd_mean_ElectronAffinity
2     44       wtd_gmean_ElectronAffinity
3     50         wtd_std_ElectronAffinity
4     60               wtd_std_FusionHeat
5     66  wtd_entropy_ThermalConductivity
6     69          std_ThermalConductivity
7     70      wtd_std_ThermalConductivity
8     80                  wtd_std_Valence 


Explained Variance Score:
RVE RFs:  0.9115
RVE DTs:  0.7683
RVE LRs:  0.6558


# best selected features by indice
selected_index = [15, 25, 44, 47, 49, 64, 67, 72, 74]

# column names of the best selected features
selected_names = list(x_test_scaled.columns[selected_index])

print("Best selected features by indice:", selected_index)
print("\nColumn names of the best selected features:\n", selected_names)

Best selected features by indice: [15, 25, 44, 47, 49, 64, 67, 72, 74]

Column names of the best selected features:
 ['entropy_fie', 'entropy_atomic_radius', 'wtd_gmean_ElectronAffinity', 'range_ElectronAffinity', 'std_ElectronAffinity', 'wtd_gmean_ThermalConductivity', 'range_ThermalConductivity', 'wtd_mean_Valence', 'wtd_gmean_Valence']


# evaluating the explained total variance with 10 principal components
pca = PCA(n_components=10, random_state=random_state)
pca.fit(x_train_scaled)

tve = 0

for i, ve in enumerate(pca.explained_variance_ratio_):
    tve += ve
    print("PC%d - Variance explained: %7.4f - Total Variance: %7.4f" % (i, ve, tve))
print()
print("Actual Eigenvalues:", pca.singular_values_, "\n")
for i, comp in enumerate(pca.components_):
    print("PC", i, "-->", comp, "\n")

PC0 - Variance explained:  0.3882 - Total Variance:  0.3882
PC1 - Variance explained:  0.1037 - Total Variance:  0.4919
PC2 - Variance explained:  0.0962 - Total Variance:  0.5881
PC3 - Variance explained:  0.0791 - Total Variance:  0.6672
PC4 - Variance explained:  0.0588 - Total Variance:  0.7260
PC5 - Variance explained:  0.0378 - Total Variance:  0.7637
PC6 - Variance explained:  0.0367 - Total Variance:  0.8004
PC7 - Variance explained:  0.0310 - Total Variance:  0.8315
PC8 - Variance explained:  0.0237 - Total Variance:  0.8552
PC9 - Variance explained:  0.0199 - Total Variance:  0.8751

Actual Eigenvalues: [668.26743995 345.36081648 332.64473513 301.55338751 260.02883809
 208.44864431 205.42801886 188.97348227 165.1789302  151.29300197] 

PC 0 --> [-0.15571443  0.05202323  0.09987778  0.08345308  0.1205011  -0.14650234
 -0.15640088 -0.12430574  0.08844361 -0.09850257 -0.11254083 -0.05576073
 -0.1285755  -0.02210194 -0.11690234 -0.15651251 -0.10941026 -0.16405123
 -0.08526872 -0.15540541 -0.16350122  0.02009301  0.11968099  0.07790363
  0.1379374  -0.15329753 -0.16349529 -0.16373978  0.10061436 -0.15000212
 -0.16057137  0.10924692  0.13144356  0.150542    0.15579175 -0.1215454
 -0.11579583 -0.07467742  0.09452822 -0.04020672 -0.07021667  0.00738102
 -0.05970996  0.05641308 -0.01208703 -0.14016098 -0.09566763 -0.10431861
 -0.0686458  -0.09193077 -0.10271663  0.09452953  0.09795477  0.11525258
  0.11533882 -0.13409699 -0.1432594   0.00301621  0.07725744  0.02049498
  0.01044684 -0.05087482 -0.02764379  0.11012691  0.10800042 -0.0338688
  0.00097751 -0.14292088 -0.05922646 -0.13392186 -0.1384527   0.13988001
  0.14496576  0.14124259  0.14699077 -0.15872666 -0.15610325 -0.02557793
  0.10859006 -0.00801483  0.00431711] 

PC 1 --> [-0.10007715 -0.22568311 -0.20193765 -0.21389395 -0.18446934 -0.12885116
 -0.08866039 -0.08872597 -0.1206912  -0.07648633 -0.059769    0.16800255
  0.12702963  0.16424139  0.1420496  -0.09967306 -0.09912997  0.02705894
  0.05187988  0.06100689  0.037385   -0.21440163 -0.18222633 -0.22417727
 -0.15696562 -0.11415286 -0.0757934   0.02087917 -0.06621921  0.07194807
  0.04761352 -0.16802647 -0.14993013 -0.11522841 -0.11098527 -0.1461729
 -0.13319516 -0.09627511 -0.10152626 -0.08054333 -0.0675886   0.09025652
  0.08281791  0.07175037  0.0869295  -0.10206557 -0.09316122  0.03910292
  0.06216073  0.05278969  0.02602499  0.12406961  0.13050566  0.05704523
  0.09253688 -0.17324491 -0.13510352  0.16044891  0.13849386  0.18002205
  0.1725903  -0.01183736 -0.05886364  0.01147741  0.00075423 -0.11703762
 -0.07450584 -0.05390645 -0.05749378 -0.03899042 -0.05805233 -0.0368641
 -0.01465001 -0.04208152 -0.01711788 -0.09841921 -0.08972819 -0.00544381
 -0.0195664   0.00507352  0.00118976] 

PC 2 --> [-0.06838743  0.02530786 -0.02606592  0.05655384 -0.00249176 -0.04953216
 -0.04147472 -0.09543285 -0.03549468 -0.10658653 -0.09150673 -0.11903039
  0.05979289 -0.13920146  0.04887637 -0.08879438 -0.19952029 -0.00564617
  0.14402891  0.0033996   0.05052261  0.12888984 -0.03955558  0.09567676
 -0.05210017 -0.08530773 -0.06875933  0.01193231 -0.00853514  0.00580134
  0.02731738 -0.04994861 -0.07679138 -0.0385445  -0.05089352 -0.07240113
 -0.13340495 -0.13163674 -0.04894742 -0.14514685 -0.11782161 -0.11813176
 -0.00583056 -0.0762996   0.02744861 -0.08429804 -0.18590506 -0.14277375
  0.05034774 -0.13012262 -0.12391992 -0.15843579 -0.15452161 -0.11821946
 -0.1298288  -0.03992937 -0.06543496 -0.20759388 -0.11421038 -0.19814035
 -0.20498357  0.07164688  0.02432294 -0.05457249 -0.06797859 -0.20016543
 -0.24322536  0.1099358   0.08182127  0.12550524  0.11632539 -0.11339568
 -0.12067322 -0.08838736 -0.10282035 -0.064449   -0.09667551 -0.22710219
 -0.04418331 -0.21173312 -0.23224443] 

PC 3 --> [-0.05234697  0.18520529  0.15294259  0.15102569  0.11290981 -0.05640258
 -0.04404021  0.07584158  0.1185149   0.10354341  0.11942657  0.15444658
  0.13833225  0.14925564  0.14762264 -0.05154492 -0.06871556  0.04955978
  0.08029329  0.07080011  0.06936597 -0.02720696 -0.05669926 -0.04249869
 -0.05902621 -0.05537858 -0.02922239  0.00156612 -0.01511607  0.01627145
  0.02888436  0.14884523  0.11133038  0.06283543  0.05482899 -0.10896707
 -0.07721367  0.1484785   0.10580346  0.17307816  0.17708532  0.26961394
  0.27291024  0.23170639  0.26508963 -0.01921644 -0.03375821  0.12068656
  0.19778374  0.14162756  0.12323819 -0.0884086  -0.09526313 -0.07148352
 -0.08834981 -0.06714433 -0.03869833 -0.11282648 -0.08232582 -0.1030554
 -0.09478307 -0.02944106 -0.06566957 -0.09822199 -0.07935789 -0.18170536
 -0.15394783  0.01701873 -0.00247522  0.03393499  0.01199676  0.10914606
  0.10781428  0.10148956  0.10573997 -0.04891729 -0.04082847  0.02810765
  0.06404954  0.04332808  0.02785903] 

PC 4 --> [ 0.01153354  0.0286572  -0.03341355 -0.00792691 -0.04706446  0.00155438
  0.00281518  0.08438901  0.0400745   0.10375905  0.06502987 -0.09860236
  0.03481754 -0.09906735  0.04297635  0.02011398 -0.07807857 -0.0214873
  0.14074166 -0.01924294 -0.00668973  0.12288563 -0.020871    0.08824059
 -0.02858658  0.01968752 -0.00411033  0.05889615  0.05285952  0.06248234
  0.04749301  0.09426437  0.06703653  0.05312411  0.04607159  0.04440118
 -0.0267611   0.13741264  0.1372824   0.14172099  0.14029016 -0.00189774
  0.10921561  0.00901535  0.12321258  0.01951418 -0.08793272 -0.06441515
  0.15272889 -0.04102058 -0.05019216  0.19171843  0.19347346  0.15912986
  0.18104983  0.04277547 -0.00633029  0.15790531  0.19635852  0.16491135
  0.14933063  0.29118832  0.29858998  0.19776006  0.2155436   0.03514672
 -0.07437284  0.14387047  0.26512451  0.15556816  0.14807464 -0.02109287
 -0.02880891 -0.00089416 -0.0108651   0.03389515 -0.01721428 -0.14030199
  0.06194528 -0.12372821 -0.16572588] 

PC 5 --> [ 0.05984263  0.05359979 -0.06812848  0.08872224 -0.03750603  0.12878478
  0.07801557 -0.06105453 -0.02634693 -0.08513599 -0.08430604 -0.20329896
  0.11952999 -0.20782112  0.13264291  0.08225211 -0.15262662 -0.04546081
  0.28331027 -0.05865748  0.01105114  0.16245507 -0.14085904  0.1615566
 -0.11748153  0.09267866  0.0538085   0.00545232  0.01438212 -0.00041682
  0.02742979  0.00358279 -0.07392536  0.06181742  0.00496169  0.17993007
  0.07988808 -0.1024617  -0.04520671 -0.13155811 -0.11030983 -0.01576622
  0.15675982  0.03719305  0.19569687  0.1288531  -0.10433029 -0.05306374
  0.24896833 -0.06449003 -0.04876823  0.03179855  0.05466549  0.02274109
  0.05129726  0.10040539  0.02451817  0.05879587  0.11948542  0.05455084
  0.05100271 -0.14629919 -0.27892861 -0.05718436 -0.12955221  0.15556646
  0.07298191 -0.05976092 -0.2094564  -0.08219321 -0.10812697  0.08223003
  0.09462144  0.07748877  0.09769753  0.07485915 -0.0502952   0.07513896
  0.21778247  0.07184818  0.01819969] 

PC 6 --> [-0.05647019  0.06788129 -0.02099803 -0.03121123 -0.09035351 -0.12668067
 -0.06193322  0.20680227  0.04943502  0.25885852  0.2411621  -0.04261144
  0.08223076 -0.0582448   0.08149477 -0.05755978 -0.11545303  0.00782242
  0.10952166  0.02802525  0.05169982  0.1030036  -0.06126197  0.06729284
 -0.06921997 -0.06261488 -0.01372363  0.04511546 -0.04622535  0.06997993
  0.0737028   0.05850626 -0.01458562 -0.03857373 -0.05985665 -0.14195272
 -0.08621206  0.25374967  0.04313465  0.28449676  0.25355476 -0.27065586
 -0.19459403 -0.21508942 -0.17035547 -0.07244016 -0.11256299 -0.16128121
 -0.07313936 -0.16394299 -0.138924    0.0206198   0.01163678  0.01138033
  0.00450602 -0.07606763 -0.04599592  0.01353014  0.02090399  0.02134712
  0.02862534 -0.13067795 -0.19871789 -0.05272286 -0.07404246 -0.00634218
  0.03980436 -0.0783434  -0.18041549 -0.08251652 -0.10479022 -0.04128462
 -0.05400736 -0.05366641 -0.06212207 -0.06512901 -0.05813585  0.06743291
 -0.01790886  0.08490599  0.07194373] 

PC 7 --> [ 2.43445348e-02 -1.32946979e-01 -3.61378326e-03 -1.19263816e-01
  9.06083756e-03  4.66308332e-02 -1.12819812e-01 -2.63322399e-02
  2.85433762e-01 -2.94282981e-02 -6.94920270e-02 -1.40713397e-02
 -4.73760974e-02 -4.30406386e-02 -5.42618419e-02  5.19393153e-02
 -3.92456098e-02  6.24151774e-02  1.54220968e-01  8.03968704e-02
 -9.44999888e-05 -3.97700339e-02  5.64254232e-02 -4.52062713e-02
  5.54131314e-02  5.23243505e-02 -8.71391291e-02  1.95011067e-02
  3.29100018e-01  3.65556035e-02 -2.55411663e-02 -1.24463570e-01
 -1.18669755e-03 -1.02992029e-01 -1.17456733e-02 -4.62606860e-03
 -1.80671752e-01 -9.03117231e-03  2.79036461e-01 -4.75238688e-03
 -6.85629603e-02 -7.03895984e-02 -4.61301570e-02 -1.24706510e-01
 -6.89698952e-02  1.42619247e-02 -8.04765897e-02  1.08131454e-01
  1.56986072e-01  1.08410733e-01  3.28293433e-02 -1.50585152e-01
 -7.02253925e-02 -1.83477726e-01 -7.48617409e-02 -2.03485309e-03
 -1.22832079e-01 -2.34992422e-02  1.03060621e-01 -1.57901767e-02
 -6.84359870e-02  4.27351000e-02  8.68207832e-02  2.00681202e-02
  8.21523777e-02  5.95189338e-02 -3.53800555e-02  8.89874476e-03
  1.51804481e-01  1.42850753e-02 -1.19278177e-02 -1.06659333e-01
 -2.19435117e-02 -1.44930485e-01 -4.38140848e-02  2.31822251e-02
 -1.04045229e-01  2.52338486e-01  3.15267154e-01  2.69492297e-01
  1.96575521e-01] 

PC 8 --> [-0.05754298 -0.06469633 -0.12481454 -0.04700495 -0.10056365 -0.05116762
  0.04489517 -0.02678454 -0.24379782 -0.02525947 -0.01720463 -0.18221097
 -0.01972601 -0.16853528 -0.00854283 -0.06657683 -0.05074627 -0.11191095
 -0.04566042 -0.11564667 -0.06609704  0.0380265  -0.07325054  0.08598266
 -0.03207774 -0.05095323  0.04010354 -0.09617416 -0.25560137 -0.1034547
 -0.07674733 -0.01882791 -0.0850737  -0.00209463 -0.03960152 -0.07388185
  0.04563768  0.08667524 -0.19545384  0.0963873   0.07971411  0.07055744
  0.11245138  0.07246184  0.08646805 -0.06099122 -0.08536765 -0.04497264
  0.06957453 -0.03117536  0.04093008 -0.07088645 -0.06828463 -0.01350569
 -0.03311193 -0.01602122  0.04082056 -0.13907726 -0.10851897 -0.1299767
 -0.1149111   0.24032716  0.14357995  0.20855297  0.17880969  0.00248776
  0.08506109  0.03999229  0.03374312  0.05145171  0.0209148   0.02874876
  0.00814253 -0.01759639 -0.02200105 -0.10754248 -0.03261032  0.2997764
 -0.08599204  0.33384645  0.30637474] 

PC 9 --> [-0.07028766  0.09096106  0.06942911  0.05122535  0.04723735 -0.06851778
  0.00723323  0.04222472 -0.07584268  0.07779925  0.07697211 -0.20746101
 -0.17474243 -0.26558065 -0.20185088 -0.06449037  0.08407146  0.05673614
 -0.16907842  0.09245452  0.00348355  0.2485373   0.16230696  0.14983295
  0.12051236 -0.07342501  0.00619989  0.15455956 -0.08964042  0.22780302
  0.10966065 -0.13484475 -0.04019354 -0.08594494 -0.04477976 -0.04352347
 -0.02269355 -0.07606402 -0.07302526 -0.08040577 -0.01470477  0.07562057
  0.07429282  0.11975716  0.08594841  0.02120252  0.06548466  0.00963733
  0.03682496  0.02684395  0.08873318 -0.02532711  0.08419298 -0.10424798
  0.04333703 -0.11373881 -0.08444405  0.13406349  0.15123959  0.15360027
  0.15099229 -0.24951174  0.05365472 -0.22618574 -0.06373507 -0.19431757
 -0.19044454 -0.04646457  0.15410843 -0.03186068  0.03204758 -0.04405679
 -0.00061464 -0.05853376 -0.01207825 -0.06364751  0.01539113  0.07536031
 -0.07796779  0.09711798  0.10857491]


pc = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
plt.plot(pc, pca.singular_values_)
plt.title("Scree Plot", fontsize=14)
plt.xlabel('Principal component', fontsize=12)
plt.ylabel('Eigenvalues', fontsize=12)

Text(0, 0.5, 'Eigenvalues')


plt.figure(figsize=(8, 6))
plt.plot(pca.explained_variance_ratio_.cumsum(), marker='o', linestyle='--')
plt.title('Explained Variance by Components')
plt.xlabel('Number of Components')
plt.ylabel('Cumulative Explained Variance')

Text(0, 0.5, 'Cumulative Explained Variance')


pca = PCA(n_components=4, random_state=random_state)
pca.fit(x_train_scaled)

nX_train = pca.transform(x_train_scaled)
nX_test = pca.transform(x_test_scaled)
naif_model_testing(nX_train, nX_test, Y_train.values.ravel(), Y_test.values.ravel())

RVE RFs:  0.8651
RVE DTs:  0.6630
RVE LRs:  0.5048


xtrain_pc = pd.DataFrame(nX_train)
xtrain_pc.columns = ["PC1", "PC2", "PC3", "PC4"]
xtrain_pc


xtest_pc = pd.DataFrame(nX_test)
xtest_pc.columns = ["PC1", "PC2", "PC3", "PC4"]
xtest_pc


# finding the best model using feature selection method
X = x_train_scaled[selected_names]
Y = Y_train.values.ravel()

X

Y

array([ 2.41 , 75.   , 24.761, ..., 60.   , 15.   ,  4.4  ])


# Linear Regression grid search - FIRST RUN ONLY
'''
key = 'Linear Regression'
algorithm = LinearRegression()
params = [{}]
print(f'Now testing {key}')
linearResult = best_model(X, Y, algorithm, params, cv=5)
linearResult = result_to_file(key, linearResult, 'appendix/linear-result-fselection.csv')
'''

"\nkey = 'Linear Regression'\nalgorithm = LinearRegression()\nparams = [{}]\nprint(f'Now testing {key}')\nlinearResult = best_model(X, Y, algorithm, params, cv=5)\nlinearResult = result_to_file(key, linearResult, 'appendix/linear-result-fselection.csv')\n"


# Decision Tree Regressor grid search - FIRST RUN ONLY
'''
key = 'Decision Tree Regressor'
algorithm = DecisionTreeRegressor()
params = [
    {
        'criterion': ['squared_error', 'friedman_mse', 'absolute_error', 'poisson'],
        'splitter': ['best', 'random'],
        'max_depth': [None, 2, 3, 4, 5],
        'min_samples_split': [2, 3, 4, 5, 6],
        'max_leaf_nodes': [None, 2, 3, 4, 5],
        'random_state': [random_state],
    }
]
print(f'Now testing {key}')
decisionTreeResult = best_model(X, Y, algorithm, params, cv=5)
decisionTreeResult = result_to_file(key, decisionTreeResult, 'appendix/decision-tree-result-fselection.csv')
'''

"\nkey = 'Decision Tree Regressor'\nalgorithm = DecisionTreeRegressor()\nparams = [\n    {\n        'criterion': ['squared_error', 'friedman_mse', 'absolute_error', 'poisson'],\n        'splitter': ['best', 'random'],\n        'max_depth': [None, 2, 3, 4, 5],\n        'min_samples_split': [2, 3, 4, 5, 6],\n        'max_leaf_nodes': [None, 2, 3, 4, 5],\n        'random_state': [random_state],\n    }\n]\nprint(f'Now testing {key}')\ndecisionTreeResult = best_model(X, Y, algorithm, params, cv=5)\ndecisionTreeResult = result_to_file(key, decisionTreeResult, 'appendix/decision-tree-result-fselection.csv')\n"


# Random Forest Regressor grid search - FIRST RUN ONLY
'''
key = 'Random Forest Regressor'
algorithm = RandomForestRegressor()
params = [
    {
        'n_estimators': [100, 500, 1000],
        'max_depth': [2, 3, 4, 5],
        'min_samples_split': [2, 3, 4],
        'max_leaf_nodes': [None, 2, 3, 4],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
random_forest_result = best_model(X, Y, algorithm, params, cv=5)
random_forest_result = result_to_file(key, random_forest_result, 'appendix/random-forest-result-fselection.csv')
'''

"\nkey = 'Random Forest Regressor'\nalgorithm = RandomForestRegressor()\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'max_depth': [2, 3, 4, 5],\n        'min_samples_split': [2, 3, 4],\n        'max_leaf_nodes': [None, 2, 3, 4],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\nrandom_forest_result = best_model(X, Y, algorithm, params, cv=5)\nrandom_forest_result = result_to_file(key, random_forest_result, 'appendix/random-forest-result-fselection.csv')\n"


# Ada Boost with Decision Tree Regressor grid search - FIRST RUN ONLY
'''
key = 'Ada Boost with Decision Tree Regressor'
algorithm = AdaBoostRegressor(base_estimator=DecisionTreeRegressor())
params = [
    {
        'n_estimators': [100, 500, 1000],
        'learning_rate': [0.2, 0.5, 0.8, 1],
        'loss': ['linear', 'square', 'exponential'],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
ada_boost_dt_result = best_model(X, Y, algorithm, params, cv=5)
ada_boost_dt_result = result_to_file(key, ada_boost_dt_result, 'appendix/ada-boost-dt-fselection.csv')
'''

"\nkey = 'Ada Boost with Decision Tree Regressor'\nalgorithm = AdaBoostRegressor(base_estimator=DecisionTreeRegressor())\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'learning_rate': [0.2, 0.5, 0.8, 1],\n        'loss': ['linear', 'square', 'exponential'],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\nada_boost_dt_result = best_model(X, Y, algorithm, params, cv=5)\nada_boost_dt_result = result_to_file(key, ada_boost_dt_result, 'appendix/ada-boost-dt-fselection.csv')\n"


# Ada Boost with Linear Regression grid search - FIRST RUN ONLY
'''
key = 'Ada Boost with Linear Regression'
algorithm = AdaBoostRegressor(base_estimator=LinearRegression())
params = [
    {
        'n_estimators': [100, 500, 1000],
        'learning_rate': [0.2, 0.5, 0.8, 1],
        'loss': ['linear', 'square', 'exponential'],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
ada_boost_lr_result = best_model(X, Y, algorithm, params, cv=5)
ada_boost_lr_result = result_to_file(key, ada_boost_lr_result, 'appendix/ada-boost-lr-fselection.csv')
'''

"\nkey = 'Ada Boost with Linear Regression'\nalgorithm = AdaBoostRegressor(base_estimator=LinearRegression())\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'learning_rate': [0.2, 0.5, 0.8, 1],\n        'loss': ['linear', 'square', 'exponential'],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\nada_boost_lr_result = best_model(X, Y, algorithm, params, cv=5)\nada_boost_lr_result = result_to_file(key, ada_boost_lr_result, 'appendix/ada-boost-lr-fselection.csv')\n"


# Gradient Boosting Regressor grid search - FIRST RUN ONLY
'''
key = 'Gradient Boosting Regressor'
algorithm = GradientBoostingRegressor()
params = [
    {
        'n_estimators': [100, 500, 1000],
        'min_samples_split': [2, 3, 4, 5],
        'max_depth': [2, 3, 4, 5],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
gradient_boosting_result = best_model(X, Y, algorithm, params, cv=5)
gradient_boosting_result = result_to_file(key, gradient_boosting_result, 'appendix/gradient-boost-fselection.csv')
'''

"\nkey = 'Gradient Boosting Regressor'\nalgorithm = GradientBoostingRegressor()\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'min_samples_split': [2, 3, 4, 5],\n        'max_depth': [2, 3, 4, 5],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\ngradient_boosting_result = best_model(X, Y, algorithm, params, cv=5)\ngradient_boosting_result = result_to_file(key, gradient_boosting_result, 'appendix/gradient-boost-fselection.csv')\n"


# reading the result output file of each estimator, and tranform into dataframe
LR_result_fs = pd.DataFrame(pd.read_csv("appendix/linear-result-fselection.csv", sep=",")).drop(columns='Unnamed: 0')
DT_result_fs = pd.DataFrame(pd.read_csv("appendix/decision-tree-result-fselection.csv", sep=",")).drop(columns='Unnamed: 0')
RF_result_fs = pd.DataFrame(pd.read_csv("appendix/random-forest-result-fselection.csv", sep=",")).drop(columns='Unnamed: 0')
Ada_LR_result_fs = pd.DataFrame(pd.read_csv("appendix/ada-boost-lr-fselection.csv", sep=",")).drop(columns='Unnamed: 0')
Ada_DT_result_fs = pd.DataFrame(pd.read_csv("appendix/ada-boost-dt-fselection.csv", sep=",")).drop(columns='Unnamed: 0')
Gradient_result_fs = pd.DataFrame(pd.read_csv("appendix/gradient-boost-fselection.csv", sep=",")).drop(columns='Unnamed: 0')

# merging all in a final results dataframe
final_results_fs= LR_result_fs.append([LR_result_fs, DT_result_fs, RF_result_fs, Ada_LR_result_fs, Ada_DT_result_fs, Gradient_result_fs], ignore_index=True)

# sorting by mean_test_score - descending
final_results_fs_sorted = final_results_fs.sort_values(by="mean_test_score", ascending=False)

# selecting the top 10 models with the best mean_test_score
final_results_fs_top10 = final_results_fs_sorted.head(10)

print("\nTop 10 best models with feature selection:\n")
final_results_fs_top10

Top 10 best models with feature selection:


# finding the best model using PCA method
X = xtrain_pc
Y = Y_train.values.ravel()


# Linear Regression grid search - FIRST RUN ONLY
'''
key = 'Linear Regression'
algorithm = LinearRegression()
params = [{}]
print(f'Now testing {key}')
linearResult = best_model(X, Y, algorithm, params, cv=5)
linearResult = result_to_file(key, linearResult, 'appendix/linear-result-PCA.csv')
'''

"\nkey = 'Linear Regression'\nalgorithm = LinearRegression()\nparams = [{}]\nprint(f'Now testing {key}')\nlinearResult = best_model(X, Y, algorithm, params, cv=5)\nlinearResult = result_to_file(key, linearResult, 'appendix/linear-result-PCA.csv')\n"


# Decision Tree Regressor grid search - FIRST RUN ONLY
'''
key = 'Decision Tree Regressor'
algorithm = DecisionTreeRegressor()
params = [
    {
        'criterion': ['squared_error', 'friedman_mse', 'absolute_error', 'poisson'],
        'splitter': ['best', 'random'],
        'max_depth': [None, 2, 3, 4, 5],
        'min_samples_split': [2, 3, 4, 5, 6],
        'max_leaf_nodes': [None, 2, 3, 4, 5],
        'random_state': [random_state],
    }
]
print(f'Now testing {key}')
decisionTreeResult = best_model(X, Y, algorithm, params, cv=5)
decisionTreeResult = result_to_file(key, decisionTreeResult, 'appendix/decision-tree-result-PCA.csv')
'''

"\nkey = 'Decision Tree Regressor'\nalgorithm = DecisionTreeRegressor()\nparams = [\n    {\n        'criterion': ['squared_error', 'friedman_mse', 'absolute_error', 'poisson'],\n        'splitter': ['best', 'random'],\n        'max_depth': [None, 2, 3, 4, 5],\n        'min_samples_split': [2, 3, 4, 5, 6],\n        'max_leaf_nodes': [None, 2, 3, 4, 5],\n        'random_state': [random_state],\n    }\n]\nprint(f'Now testing {key}')\ndecisionTreeResult = best_model(X, Y, algorithm, params, cv=5)\ndecisionTreeResult = result_to_file(key, decisionTreeResult, 'appendix/decision-tree-result-PCA.csv')\n"


# Random Forest Regressor grid search - FIRST RUN ONLY
'''
key = 'Random Forest Regressor'
algorithm = RandomForestRegressor()
params = [
    {
        'n_estimators': [100, 500, 1000],
        'max_depth': [2, 3, 4, 5],
        'min_samples_split': [2, 3, 4],
        'max_leaf_nodes': [None, 2, 3, 4],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
random_forest_result = best_model(X, Y, algorithm, params, cv=5)
random_forest_result = result_to_file(key, random_forest_result, 'appendix/random-forest-result-PCA.csv')
'''

"\nkey = 'Random Forest Regressor'\nalgorithm = RandomForestRegressor()\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'max_depth': [2, 3, 4, 5],\n        'min_samples_split': [2, 3, 4],\n        'max_leaf_nodes': [None, 2, 3, 4],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\nrandom_forest_result = best_model(X, Y, algorithm, params, cv=5)\nrandom_forest_result = result_to_file(key, random_forest_result, 'appendix/random-forest-result-PCA.csv')\n"


# Ada Boost with Decision Tree Regressor grid search - FIRST RUN ONLY
'''
key = 'Ada Boost with Decision Tree Regressor'
algorithm = AdaBoostRegressor(base_estimator=DecisionTreeRegressor())
params = [
    {
        'n_estimators': [100, 500, 1000],
        'learning_rate': [0.2, 0.5, 0.8, 1],
        'loss': ['linear', 'square', 'exponential'],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
ada_boost_dt_result = best_model(X, Y, algorithm, params, cv=5)
ada_boost_dt_result = result_to_file(key, ada_boost_dt_result, 'appendix/ada-boost-dt-PCA.csv')
'''

"\nkey = 'Ada Boost with Decision Tree Regressor'\nalgorithm = AdaBoostRegressor(base_estimator=DecisionTreeRegressor())\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'learning_rate': [0.2, 0.5, 0.8, 1],\n        'loss': ['linear', 'square', 'exponential'],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\nada_boost_dt_result = best_model(X, Y, algorithm, params, cv=5)\nada_boost_dt_result = result_to_file(key, ada_boost_dt_result, 'appendix/ada-boost-dt-PCA.csv')\n"


# Ada Boost with Linear Regression grid search - FIRST RUN ONLY
'''
key = 'Ada Boost with Linear Regression'
algorithm = AdaBoostRegressor(base_estimator=LinearRegression())
params = [
    {
        'n_estimators': [100, 500, 1000],
        'learning_rate': [0.2, 0.5, 0.8, 1],
        'loss': ['linear', 'square', 'exponential'],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
ada_boost_lr_result = best_model(X, Y, algorithm, params, cv=5)
ada_boost_lr_result = result_to_file(key, ada_boost_lr_result, 'appendix/ada-boost-lr-PCA.csv')
'''

"\nkey = 'Ada Boost with Linear Regression'\nalgorithm = AdaBoostRegressor(base_estimator=LinearRegression())\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'learning_rate': [0.2, 0.5, 0.8, 1],\n        'loss': ['linear', 'square', 'exponential'],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\nada_boost_lr_result = best_model(X, Y, algorithm, params, cv=5)\nada_boost_lr_result = result_to_file(key, ada_boost_lr_result, 'appendix/ada-boost-lr-PCA.csv')\n"


# Gradient Boosting Regressor grid search - FIRST RUN ONLY
'''
key = 'Gradient Boosting Regressor'
algorithm = GradientBoostingRegressor()
params = [
    {
        'n_estimators': [100, 500, 1000],
        'min_samples_split': [2, 3, 4, 5],
        'max_depth': [2, 3, 4, 5],
        'random_state': [random_state]
    }
]
print(f'Now testing {key}')
gradient_boosting_result = best_model(X, Y, algorithm, params, cv=5)
gradient_boosting_result = result_to_file(key, gradient_boosting_result, 'appendix/gradient-boost-PCA.csv')
'''

"\nkey = 'Gradient Boosting Regressor'\nalgorithm = GradientBoostingRegressor()\nparams = [\n    {\n        'n_estimators': [100, 500, 1000],\n        'min_samples_split': [2, 3, 4, 5],\n        'max_depth': [2, 3, 4, 5],\n        'random_state': [random_state]\n    }\n]\nprint(f'Now testing {key}')\ngradient_boosting_result = best_model(X, Y, algorithm, params, cv=5)\ngradient_boosting_result = result_to_file(key, gradient_boosting_result, 'appendix/gradient-boost-PCA.csv')\n"


# reading the result output file of each estimator, and tranform into dataframe
LR_result_pca = pd.DataFrame(pd.read_csv("appendix/linear-result-PCA.csv", sep=",")).drop(columns='Unnamed: 0')
DT_result_pca = pd.DataFrame(pd.read_csv("appendix/decision-tree-result-PCA.csv", sep=",")).drop(columns='Unnamed: 0')
RF_result_pca = pd.DataFrame(pd.read_csv("appendix/random-forest-result-PCA.csv", sep=",")).drop(columns='Unnamed: 0')
Ada_LR_result_pca = pd.DataFrame(pd.read_csv("appendix/ada-boost-lr-PCA.csv", sep=",")).drop(columns='Unnamed: 0')
Ada_DT_result_pca = pd.DataFrame(pd.read_csv("appendix/ada-boost-dt-PCA.csv", sep=",")).drop(columns='Unnamed: 0')
Gradient_result_pca = pd.DataFrame(pd.read_csv("appendix/gradient-boost-PCA.csv", sep=",")).drop(columns='Unnamed: 0')

# merging all in a final results dataframe
final_results_pca = LR_result_pca.append([LR_result_pca, DT_result_pca, RF_result_pca, Ada_LR_result_pca, Ada_DT_result_pca, Gradient_result_pca], ignore_index=True)

# sorting by mean_test_score - descending
final_results_pc_sorted = final_results_pca.sort_values(by="mean_test_score", ascending=False)

# selecting the top 10 models with the best mean_test_score
final_results_pc_top10 = final_results_pc_sorted.head(10)

print("\nTop 10 best models with Principal Components:\n")
final_results_pc_top10

Top 10 best models with Principal Components:


final_results_fs_top10.head(1)


# training the best model for features selection set
reg = GradientBoostingRegressor(max_depth=5, min_samples_split=5, n_estimators=1000, random_state=random_state)
reg = reg.fit(x_train_scaled[selected_names], Y_train.values.ravel())
reg.predict(x_test_scaled[selected_names])
R2 = reg.score(x_test_scaled[selected_names], Y_test)

print("\nR2 - Coefficient of determination of the prediction for the best features selected is: ", R2)

R2 - Coefficient of determination of the prediction for the best features selected is:  0.9056962393750775


final_results_pc_top10.head(1)


# training the best model for principal components set
reg = AdaBoostRegressor(base_estimator=DecisionTreeRegressor(),learning_rate=0.2, loss='square', n_estimators=100, random_state=random_state)
reg = reg.fit(xtrain_pc, Y_train.values.ravel())
reg.predict(xtest_pc)
R2 = reg.score(xtest_pc, Y_test)

print("\nR2 - Coefficient of determination of the prediction for the principal components is: ", R2)

R2 - Coefficient of determination of the prediction for the principal components is:  0.8590995898302416

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence	critical_temp
0	4	88.944468	57.862692	66.361592	36.116612	1.181795	1.062396	122.90607	31.794921	51.968828	53.622535	775.425000	1010.268571	718.152900	938.016780	1.305967	0.791488	810.6	735.985714	323.811808	355.562967	160.250000	105.514286	136.126003	84.528423	1.259244	1.207040	205	42.914286	75.237540	69.235569	4654.35725	2961.502286	724.953211	53.543811	1.033129	0.814598	8958.571	1579.583429	3306.162897	3572.596624	81.837500	111.727143	60.123179	99.414682	1.159687	0.787382	127.05	80.987143	51.433712	42.558396	6.905500	3.846857	3.479475	1.040986	1.088575	0.994998	12.878	1.744571	4.599064	4.666920	107.756645	61.015189	7.062488	0.621979	0.308148	0.262848	399.97342	57.127669	168.854244	138.517163	2.25	2.257143	2.213364	2.219783	1.368922	1.066221	1	1.085714	0.433013	0.437059	29.00
1	5	92.729214	58.518416	73.132787	36.396602	1.449309	1.057755	122.90607	36.161939	47.094633	53.979870	766.440000	1010.612857	720.605511	938.745413	1.544145	0.807078	810.6	743.164286	290.183029	354.963511	161.200000	104.971429	141.465215	84.370167	1.508328	1.204115	205	50.571429	67.321319	68.008817	5821.48580	3021.016571	1237.095080	54.095718	1.314442	0.914802	10488.571	1667.383429	3767.403176	3632.649185	90.890000	112.316429	69.833315	101.166398	1.427997	0.838666	127.05	81.207857	49.438167	41.667621	7.784400	3.796857	4.403790	1.035251	1.374977	1.073094	12.878	1.595714	4.473363	4.603000	172.205316	61.372331	16.064228	0.619735	0.847404	0.567706	429.97342	51.413383	198.554600	139.630922	2.00	2.257143	1.888175	2.210679	1.557113	1.047221	2	1.128571	0.632456	0.468606	26.00
2	4	88.944468	57.885242	66.361592	36.122509	1.181795	0.975980	122.90607	35.741099	51.968828	53.656268	775.425000	1010.820000	718.152900	939.009036	1.305967	0.773620	810.6	743.164286	323.811808	354.804183	160.250000	104.685714	136.126003	84.214573	1.259244	1.132547	205	49.314286	75.237540	67.797712	4654.35725	2999.159429	724.953211	53.974022	1.033129	0.760305	8958.571	1667.383429	3306.162897	3592.019281	81.837500	112.213571	60.123179	101.082152	1.159687	0.786007	127.05	81.207857	51.433712	41.639878	6.905500	3.822571	3.479475	1.037439	1.088575	0.927479	12.878	1.757143	4.599064	4.649635	107.756645	60.943760	7.062488	0.619095	0.308148	0.250477	399.97342	57.127669	168.854244	138.540613	2.25	2.271429	2.213364	2.232679	1.368922	1.029175	1	1.114286	0.433013	0.444697	19.00
3	4	88.944468	57.873967	66.361592	36.119560	1.181795	1.022291	122.90607	33.768010	51.968828	53.639405	775.425000	1010.544286	718.152900	938.512777	1.305967	0.783207	810.6	739.575000	323.811808	355.183884	160.250000	105.100000	136.126003	84.371352	1.259244	1.173033	205	46.114286	75.237540	68.521665	4654.35725	2980.330857	724.953211	53.758486	1.033129	0.788889	8958.571	1623.483429	3306.162897	3582.370597	81.837500	111.970357	60.123179	100.244950	1.159687	0.786900	127.05	81.097500	51.433712	42.102344	6.905500	3.834714	3.479475	1.039211	1.088575	0.964031	12.878	1.744571	4.599064	4.658301	107.756645	60.979474	7.062488	0.620535	0.308148	0.257045	399.97342	57.127669	168.854244	138.528893	2.25	2.264286	2.213364	2.226222	1.368922	1.048834	1	1.100000	0.433013	0.440952	22.00
4	4	88.944468	57.840143	66.361592	36.110716	1.181795	1.129224	122.90607	27.848743	51.968828	53.588771	775.425000	1009.717143	718.152900	937.025573	1.305967	0.805230	810.6	728.807143	323.811808	356.319281	160.250000	106.342857	136.126003	84.843442	1.259244	1.261194	205	36.514286	75.237540	70.634448	4654.35725	2923.845143	724.953211	53.117029	1.033129	0.859811	8958.571	1491.783429	3306.162897	3552.668664	81.837500	111.240714	60.123179	97.774719	1.159687	0.787396	127.05	80.766429	51.433712	43.452059	6.905500	3.871143	3.479475	1.044545	1.088575	1.044970	12.878	1.744571	4.599064	4.684014	107.756645	61.086617	7.062488	0.624878	0.308148	0.272820	399.97342	57.127669	168.854244	138.493671	2.25	2.242857	2.213364	2.206963	1.368922	1.096052	1	1.057143	0.433013	0.428809	23.00
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
21258	4	106.957877	53.095769	82.515384	43.135565	1.177145	1.254119	146.88130	15.504479	65.764081	43.202659	661.775000	753.793333	651.611213	750.570867	1.371139	0.927050	273.0	427.546667	114.383355	64.428777	176.500000	138.244444	169.947614	134.233861	1.350879	1.112222	111	57.808889	45.883003	35.811330	7341.25000	4963.928889	6404.741690	4082.735787	1.284617	1.110551	7511.000	2449.715556	2981.637585	2978.412680	63.825000	86.511111	49.825259	61.057784	1.164382	0.511822	117.90	74.140000	43.467883	55.219027	25.700000	34.448000	22.494622	29.041737	1.245563	0.631341	36.400	27.497778	14.446107	17.657417	65.500000	111.537778	42.371302	95.001493	1.029002	0.634332	134.00000	83.048889	55.056789	46.595943	3.25	3.555556	3.223710	3.519911	1.377820	0.913658	1	2.168889	0.433013	0.496904	2.44
21259	5	92.266740	49.021367	64.812662	32.867748	1.323287	1.571630	188.38390	7.353333	69.232655	50.148287	747.780000	989.819048	702.115184	923.426093	1.541006	0.988470	810.6	659.771429	293.286136	345.450969	159.200000	112.000000	139.743372	89.633687	1.507321	1.536691	205	20.285714	67.211309	72.795212	5174.28580	2827.415190	962.364248	66.286408	1.165065	1.080432	11848.571	1705.918143	4506.895480	3937.105612	60.484000	100.490952	29.177546	60.814837	1.112639	0.693424	138.63	74.090000	58.434336	57.634544	6.812400	4.793429	3.839585	1.315769	1.345508	1.203223	12.878	2.378952	4.340205	5.204855	132.805316	108.680590	17.747413	1.577047	0.949904	0.745515	399.97342	76.176553	151.164639	156.558695	2.20	2.047619	2.168944	2.038991	1.594167	1.337246	1	0.904762	0.400000	0.212959	122.10
21260	2	99.663190	95.609104	99.433882	95.464320	0.690847	0.530198	13.51362	53.041104	6.756810	5.405448	733.550000	691.580000	730.207231	689.480961	0.688594	0.542120	139.9	370.180000	69.950000	55.960000	183.500000	192.200000	182.926215	191.826893	0.690022	0.465055	29	124.600000	14.500000	11.600000	10296.50000	9260.600000	10150.719679	9170.377777	0.679023	0.572700	3453.000	4451.400000	1726.500000	1381.200000	71.400000	81.120000	69.537903	79.871364	0.667182	0.397810	32.40	59.040000	16.200000	12.960000	21.750000	24.780000	21.155614	24.380978	0.665945	0.395385	10.100	18.100000	5.050000	4.040000	62.500000	57.400000	61.919302	57.038314	0.683870	0.559446	17.00000	29.000000	8.500000	6.800000	4.50	4.800000	4.472136	4.781762	0.686962	0.450561	1	3.200000	0.500000	0.400000	1.98
21261	2	99.663190	97.095602	99.433882	96.901083	0.690847	0.640883	13.51362	31.115202	6.756810	6.249958	733.550000	706.969000	730.207231	704.143255	0.688594	0.648876	139.9	208.799000	69.950000	64.702805	183.500000	189.010000	182.926215	188.514109	0.690022	0.590271	29	84.230000	14.500000	13.412304	10296.50000	9640.430000	10150.719679	9518.329826	0.679023	0.667210	3453.000	2186.170000	1726.500000	1596.989169	71.400000	77.556000	69.537903	75.915236	0.667182	0.527718	32.40	43.332000	16.200000	14.984781	21.750000	23.669000	21.155614	23.144890	0.665945	0.525289	10.100	13.315000	5.050000	4.671182	62.500000	59.270000	61.919302	58.781651	0.683870	0.659671	17.00000	15.250000	8.500000	7.862385	4.50	4.690000	4.472136	4.665819	0.686962	0.577601	1	2.210000	0.500000	0.462493	1.84
21262	3	87.468333	86.858500	82.555758	80.458722	1.041270	0.895229	71.75500	43.144000	29.905282	33.927941	856.166667	821.190000	852.858789	818.631908	1.094784	0.968771	181.3	285.510000	74.569624	65.291691	127.333333	137.500000	125.493812	136.084313	1.084025	0.883461	53	67.700000	21.853045	19.345542	6311.00000	6914.900000	6186.508901	6830.731801	1.078970	0.874139	3055.000	3455.100000	1248.208583	1039.909655	135.133333	104.930000	86.530864	57.563783	0.839248	0.747947	179.30	68.080000	83.414480	87.740504	12.233333	14.440000	10.925390	13.816376	1.002899	0.826780	12.100	6.460000	5.062498	3.481724	27.506667	40.752000	4.976422	12.919996	0.194158	0.142553	78.48000	39.448000	36.425359	38.254432	5.00	4.500000	4.762203	4.242641	1.054920	0.970116	3	1.800000	1.414214	1.500000	12.80

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence	critical_temp
count	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000	21197.000000
mean	4.120300	87.544201	72.945331	71.253164	58.474874	1.166782	1.065103	115.751945	33.204053	44.436401	41.490888	769.763322	870.845514	737.547500	833.083589	1.300496	0.927436	573.413988	483.935313	216.035193	224.476880	157.968942	134.637733	144.407310	120.880069	1.269041	1.132479	139.552012	51.290519	51.669299	52.410878	6104.949112	5259.357685	3448.167503	3104.482658	1.073272	0.856543	8673.258150	2900.587194	3418.704041	3321.751640	76.866669	92.749248	54.307039	72.413486	1.071182	0.771238	120.868857	59.383115	48.956611	44.445791	14.259618	13.798017	10.102742	10.097794	1.094502	0.915214	21.109508	8.183450	8.306107	7.698272	89.762371	81.597376	29.765853	27.233552	0.727696	0.539749	251.401535	62.118953	99.127605	96.419168	3.194431	3.148856	3.052542	3.051485	1.297020	1.053977	2.042553	1.480890	0.839692	0.674168	34.494532
std	1.438282	29.643136	33.460789	30.990774	36.615381	0.364712	0.401225	54.584784	26.966285	20.019732	19.973773	87.486110	143.208996	78.345068	119.722906	0.381597	0.334107	309.205105	224.068070	109.820525	127.811013	20.151776	28.777408	22.080187	35.801133	0.375109	0.406876	67.202224	34.993536	22.876341	25.271459	2841.463086	3216.978402	3697.026215	3970.072718	0.342333	0.319808	4093.005329	2398.872994	1671.437273	1609.618632	27.695062	32.282257	29.000902	31.666733	0.343299	0.286020	58.679836	28.598854	21.728055	20.417285	11.277476	14.236516	10.049735	13.116642	0.375772	0.369882	20.321781	11.360991	8.645704	7.240884	38.514224	45.554545	34.054177	40.207155	0.326196	0.318411	158.612185	43.135044	60.108851	63.694958	1.043256	1.189878	1.044637	1.173221	0.392834	0.380121	1.243242	0.977545	0.485002	0.456038	34.276465
min	1.000000	6.941000	6.423452	5.320573	1.960849	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	375.500000	375.500000	375.500000	375.500000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	48.000000	48.000000	48.000000	48.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.429000	1.429000	1.429000	0.686245	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.500000	1.500000	1.500000	1.500000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.222000	0.222000	0.222000	0.222000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.026580	0.026580	0.026580	0.022952	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	1.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000210
25%	3.000000	72.522475	52.143839	58.041225	35.247208	0.972995	0.781227	78.899680	16.799962	32.890369	28.546294	723.740000	739.184286	692.541331	720.169563	1.086113	0.756078	268.700000	291.268750	114.800000	94.070916	149.333333	112.120370	133.542493	89.204853	1.067279	0.857598	81.000000	28.566667	35.524639	32.270972	4513.500000	2998.573742	883.117278	66.735645	0.914705	0.689062	6648.000000	1656.489126	2832.147163	2571.811460	62.090000	73.395504	33.700512	50.763699	0.894571	0.661414	87.350000	34.074637	38.625000	33.540079	7.588667	5.030667	4.109878	1.321903	0.839985	0.674190	12.878000	2.325831	4.261340	4.603000	61.000000	54.250000	8.339818	1.087095	0.457810	0.250196	87.000000	29.440000	38.002924	31.999086	2.333333	2.116279	2.267933	2.090896	1.060857	0.778998	1.000000	0.921250	0.451754	0.306892	5.380000
50%	4.000000	84.922750	60.689236	66.361592	39.873869	1.199541	1.148465	122.906070	26.601500	45.123500	44.290157	765.200000	890.787826	728.058342	856.752075	1.359251	0.917130	764.100000	511.750000	266.779102	258.776561	160.250000	125.873918	142.807563	113.170060	1.332739	1.244600	171.000000	42.960000	58.663106	60.139975	5329.085800	4285.625500	1338.878207	1500.233024	1.090610	0.883398	8958.571000	2082.956581	3303.278324	3626.410300	73.100000	102.960846	51.437518	73.173958	1.138284	0.781612	127.050000	71.159700	51.125720	48.046579	9.304400	8.303077	5.237518	4.897999	1.112098	0.996004	12.878000	3.424434	4.948155	5.498409	96.605316	73.447753	14.287643	6.089571	0.738694	0.545019	399.973420	56.556240	135.782279	115.035273	2.833333	2.605455	2.615321	2.428047	1.368922	1.169665	2.000000	1.062857	0.800000	0.500000	20.000000
75%	5.000000	100.374260	85.982703	78.019689	73.056021	1.444537	1.360388	154.119320	38.336200	59.356406	53.634945	796.320000	1004.170714	765.715174	937.613187	1.551446	1.061987	810.600000	690.784000	297.946646	342.678223	169.800000	158.206107	155.938199	150.840017	1.512410	1.426131	205.000000	60.000000	69.424491	73.810265	6718.285800	6403.916667	5770.285523	5737.162403	1.323930	1.081805	9778.571000	3395.786667	4004.273231	3959.281462	85.325000	110.738462	67.019848	89.995989	1.347292	0.877792	138.630000	76.706965	56.322245	53.318555	17.050000	18.460000	13.573422	16.410484	1.378110	1.157944	23.200000	10.447600	9.038106	8.015532	111.005316	99.075851	41.833001	47.107534	0.962398	0.777359	399.973420	91.876282	153.876488	162.810294	4.000000	4.007317	3.662842	3.909523	1.589027	1.331531	3.000000	1.910400	1.200000	1.021023	63.000000
max	9.000000	208.980400	208.980400	208.980400	208.980400	1.983797	1.958203	207.972460	205.589910	101.019700	101.019700	1313.100000	1348.028986	1313.100000	1327.593381	2.157777	2.038560	1304.500000	1251.855072	499.671949	479.162305	298.000000	298.000000	298.000000	298.000000	2.141961	1.903748	256.000000	240.164344	115.500000	97.140711	22590.000000	22590.000000	22590.000000	22590.000000	1.954297	1.703420	22588.571000	22434.160000	10724.374500	10410.932005	326.100000	326.100000	326.100000	326.100000	1.767732	1.675400	349.000000	218.696600	162.895331	169.075862	105.000000	105.000000	105.000000	105.000000	2.034410	1.747165	104.778000	102.675000	51.635000	51.680482	332.500000	406.960000	317.883627	376.032878	1.633977	1.612989	429.974170	401.440000	214.986150	213.300452	7.000000	7.000000	7.000000	7.000000	2.141963	1.949739	6.000000	6.992200	3.000000	3.000000	185.000000

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence
0	4	88.944468	57.862692	66.361592	36.116612	1.181795	1.062396	122.90607	31.794921	51.968828	53.622535	775.425000	1010.268571	718.152900	938.016780	1.305967	0.791488	810.6	735.985714	323.811808	355.562967	160.250000	105.514286	136.126003	84.528423	1.259244	1.207040	205	42.914286	75.237540	69.235569	4654.35725	2961.502286	724.953211	53.543811	1.033129	0.814598	8958.571	1579.583429	3306.162897	3572.596624	81.837500	111.727143	60.123179	99.414682	1.159687	0.787382	127.05	80.987143	51.433712	42.558396	6.905500	3.846857	3.479475	1.040986	1.088575	0.994998	12.878	1.744571	4.599064	4.666920	107.756645	61.015189	7.062488	0.621979	0.308148	0.262848	399.97342	57.127669	168.854244	138.517163	2.25	2.257143	2.213364	2.219783	1.368922	1.066221	1	1.085714	0.433013	0.437059
1	5	92.729214	58.518416	73.132787	36.396602	1.449309	1.057755	122.90607	36.161939	47.094633	53.979870	766.440000	1010.612857	720.605511	938.745413	1.544145	0.807078	810.6	743.164286	290.183029	354.963511	161.200000	104.971429	141.465215	84.370167	1.508328	1.204115	205	50.571429	67.321319	68.008817	5821.48580	3021.016571	1237.095080	54.095718	1.314442	0.914802	10488.571	1667.383429	3767.403176	3632.649185	90.890000	112.316429	69.833315	101.166398	1.427997	0.838666	127.05	81.207857	49.438167	41.667621	7.784400	3.796857	4.403790	1.035251	1.374977	1.073094	12.878	1.595714	4.473363	4.603000	172.205316	61.372331	16.064228	0.619735	0.847404	0.567706	429.97342	51.413383	198.554600	139.630922	2.00	2.257143	1.888175	2.210679	1.557113	1.047221	2	1.128571	0.632456	0.468606
2	4	88.944468	57.885242	66.361592	36.122509	1.181795	0.975980	122.90607	35.741099	51.968828	53.656268	775.425000	1010.820000	718.152900	939.009036	1.305967	0.773620	810.6	743.164286	323.811808	354.804183	160.250000	104.685714	136.126003	84.214573	1.259244	1.132547	205	49.314286	75.237540	67.797712	4654.35725	2999.159429	724.953211	53.974022	1.033129	0.760305	8958.571	1667.383429	3306.162897	3592.019281	81.837500	112.213571	60.123179	101.082152	1.159687	0.786007	127.05	81.207857	51.433712	41.639878	6.905500	3.822571	3.479475	1.037439	1.088575	0.927479	12.878	1.757143	4.599064	4.649635	107.756645	60.943760	7.062488	0.619095	0.308148	0.250477	399.97342	57.127669	168.854244	138.540613	2.25	2.271429	2.213364	2.232679	1.368922	1.029175	1	1.114286	0.433013	0.444697
3	4	88.944468	57.873967	66.361592	36.119560	1.181795	1.022291	122.90607	33.768010	51.968828	53.639405	775.425000	1010.544286	718.152900	938.512777	1.305967	0.783207	810.6	739.575000	323.811808	355.183884	160.250000	105.100000	136.126003	84.371352	1.259244	1.173033	205	46.114286	75.237540	68.521665	4654.35725	2980.330857	724.953211	53.758486	1.033129	0.788889	8958.571	1623.483429	3306.162897	3582.370597	81.837500	111.970357	60.123179	100.244950	1.159687	0.786900	127.05	81.097500	51.433712	42.102344	6.905500	3.834714	3.479475	1.039211	1.088575	0.964031	12.878	1.744571	4.599064	4.658301	107.756645	60.979474	7.062488	0.620535	0.308148	0.257045	399.97342	57.127669	168.854244	138.528893	2.25	2.264286	2.213364	2.226222	1.368922	1.048834	1	1.100000	0.433013	0.440952
4	4	88.944468	57.840143	66.361592	36.110716	1.181795	1.129224	122.90607	27.848743	51.968828	53.588771	775.425000	1009.717143	718.152900	937.025573	1.305967	0.805230	810.6	728.807143	323.811808	356.319281	160.250000	106.342857	136.126003	84.843442	1.259244	1.261194	205	36.514286	75.237540	70.634448	4654.35725	2923.845143	724.953211	53.117029	1.033129	0.859811	8958.571	1491.783429	3306.162897	3552.668664	81.837500	111.240714	60.123179	97.774719	1.159687	0.787396	127.05	80.766429	51.433712	43.452059	6.905500	3.871143	3.479475	1.044545	1.088575	1.044970	12.878	1.744571	4.599064	4.684014	107.756645	61.086617	7.062488	0.624878	0.308148	0.272820	399.97342	57.127669	168.854244	138.493671	2.25	2.242857	2.213364	2.206963	1.368922	1.096052	1	1.057143	0.433013	0.428809
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
21258	4	106.957877	53.095769	82.515384	43.135565	1.177145	1.254119	146.88130	15.504479	65.764081	43.202659	661.775000	753.793333	651.611213	750.570867	1.371139	0.927050	273.0	427.546667	114.383355	64.428777	176.500000	138.244444	169.947614	134.233861	1.350879	1.112222	111	57.808889	45.883003	35.811330	7341.25000	4963.928889	6404.741690	4082.735787	1.284617	1.110551	7511.000	2449.715556	2981.637585	2978.412680	63.825000	86.511111	49.825259	61.057784	1.164382	0.511822	117.90	74.140000	43.467883	55.219027	25.700000	34.448000	22.494622	29.041737	1.245563	0.631341	36.400	27.497778	14.446107	17.657417	65.500000	111.537778	42.371302	95.001493	1.029002	0.634332	134.00000	83.048889	55.056789	46.595943	3.25	3.555556	3.223710	3.519911	1.377820	0.913658	1	2.168889	0.433013	0.496904
21259	5	92.266740	49.021367	64.812662	32.867748	1.323287	1.571630	188.38390	7.353333	69.232655	50.148287	747.780000	989.819048	702.115184	923.426093	1.541006	0.988470	810.6	659.771429	293.286136	345.450969	159.200000	112.000000	139.743372	89.633687	1.507321	1.536691	205	20.285714	67.211309	72.795212	5174.28580	2827.415190	962.364248	66.286408	1.165065	1.080432	11848.571	1705.918143	4506.895480	3937.105612	60.484000	100.490952	29.177546	60.814837	1.112639	0.693424	138.63	74.090000	58.434336	57.634544	6.812400	4.793429	3.839585	1.315769	1.345508	1.203223	12.878	2.378952	4.340205	5.204855	132.805316	108.680590	17.747413	1.577047	0.949904	0.745515	399.97342	76.176553	151.164639	156.558695	2.20	2.047619	2.168944	2.038991	1.594167	1.337246	1	0.904762	0.400000	0.212959
21260	2	99.663190	95.609104	99.433882	95.464320	0.690847	0.530198	13.51362	53.041104	6.756810	5.405448	733.550000	691.580000	730.207231	689.480961	0.688594	0.542120	139.9	370.180000	69.950000	55.960000	183.500000	192.200000	182.926215	191.826893	0.690022	0.465055	29	124.600000	14.500000	11.600000	10296.50000	9260.600000	10150.719679	9170.377777	0.679023	0.572700	3453.000	4451.400000	1726.500000	1381.200000	71.400000	81.120000	69.537903	79.871364	0.667182	0.397810	32.40	59.040000	16.200000	12.960000	21.750000	24.780000	21.155614	24.380978	0.665945	0.395385	10.100	18.100000	5.050000	4.040000	62.500000	57.400000	61.919302	57.038314	0.683870	0.559446	17.00000	29.000000	8.500000	6.800000	4.50	4.800000	4.472136	4.781762	0.686962	0.450561	1	3.200000	0.500000	0.400000
21261	2	99.663190	97.095602	99.433882	96.901083	0.690847	0.640883	13.51362	31.115202	6.756810	6.249958	733.550000	706.969000	730.207231	704.143255	0.688594	0.648876	139.9	208.799000	69.950000	64.702805	183.500000	189.010000	182.926215	188.514109	0.690022	0.590271	29	84.230000	14.500000	13.412304	10296.50000	9640.430000	10150.719679	9518.329826	0.679023	0.667210	3453.000	2186.170000	1726.500000	1596.989169	71.400000	77.556000	69.537903	75.915236	0.667182	0.527718	32.40	43.332000	16.200000	14.984781	21.750000	23.669000	21.155614	23.144890	0.665945	0.525289	10.100	13.315000	5.050000	4.671182	62.500000	59.270000	61.919302	58.781651	0.683870	0.659671	17.00000	15.250000	8.500000	7.862385	4.50	4.690000	4.472136	4.665819	0.686962	0.577601	1	2.210000	0.500000	0.462493
21262	3	87.468333	86.858500	82.555758	80.458722	1.041270	0.895229	71.75500	43.144000	29.905282	33.927941	856.166667	821.190000	852.858789	818.631908	1.094784	0.968771	181.3	285.510000	74.569624	65.291691	127.333333	137.500000	125.493812	136.084313	1.084025	0.883461	53	67.700000	21.853045	19.345542	6311.00000	6914.900000	6186.508901	6830.731801	1.078970	0.874139	3055.000	3455.100000	1248.208583	1039.909655	135.133333	104.930000	86.530864	57.563783	0.839248	0.747947	179.30	68.080000	83.414480	87.740504	12.233333	14.440000	10.925390	13.816376	1.002899	0.826780	12.100	6.460000	5.062498	3.481724	27.506667	40.752000	4.976422	12.919996	0.194158	0.142553	78.48000	39.448000	36.425359	38.254432	5.00	4.500000	4.762203	4.242641	1.054920	0.970116	3	1.800000	1.414214	1.500000

	critical_temp
0	29.00
1	26.00
2	19.00
3	22.00
4	23.00
...	...
21258	2.44
21259	122.10
21260	1.98
21261	1.84
21262	12.80

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence
0	-0.782197	1.355194	2.180013	1.442480	2.280814	-0.432528	-0.794273	0.229753	1.727512	0.397807	-0.403240	0.655526	-0.042104	1.114707	0.263273	-0.539547	-0.552544	-1.454721	0.241337	-1.438226	-1.588450	-0.426225	0.258402	0.144156	0.528668	-0.490985	-0.815531	-1.231549	0.677758	-1.235690	-1.031048	2.273734	1.950002	1.987333	1.616745	-0.370376	-0.330099	1.851766	1.672875	2.209485	2.626139	2.805334	2.597498	3.350898	3.242455	0.021738	-0.296389	-0.836299	2.117532	-0.902095	-1.154572	0.415185	0.449956	0.798697	0.737603	-0.096700	-0.396105	-0.405162	0.246150	-0.342602	-0.495874	2.452239	-0.405501	0.784876	-0.370198	-0.340902	0.295008	0.918076	-0.364187	1.076985	-0.072416	1.406508	2.279004	1.056995	2.328312	-0.748984	-0.963929	1.564077	2.381904	2.145551	0.057192
1	0.610304	0.057860	-0.627894	-0.022547	-0.636824	0.762305	0.810130	0.160989	-0.530300	0.118091	0.184703	-0.336711	0.921017	-0.577064	0.857495	0.617919	-0.063367	0.767899	0.964575	0.753193	0.937594	1.150132	-0.683358	0.526940	-0.869147	0.613529	0.707225	0.977086	-0.462184	1.102327	1.094862	-0.489582	-0.707665	-0.645007	-0.764769	0.731538	0.136613	0.061310	-0.350593	-0.247333	0.202321	-0.174367	0.517644	-0.045471	0.465773	0.831838	0.043179	0.106084	0.583908	0.054989	0.223364	-0.560185	-0.608495	-0.554588	-0.669810	0.762365	0.479294	-0.406257	-0.468284	-0.448315	-0.292162	-0.005093	0.321320	-0.626997	-0.650682	-0.826510	-1.052709	0.936842	0.696304	0.934583	1.102727	-0.571631	-0.890798	-0.538089	-0.836259	0.681403	0.580612	-0.042364	-0.479201	-0.089027	-0.743135
2	-1.478448	0.102857	0.639025	0.582157	0.944713	-1.346449	-1.141501	-1.546072	0.186206	-1.435362	-1.319149	1.198031	-0.096001	1.709973	0.178574	-1.606182	-0.754384	-1.394186	-1.492810	-1.318748	-1.218275	-0.816166	0.477226	-0.252185	0.696353	-1.592084	-1.316214	-1.261396	0.337617	-1.059031	-1.023575	0.970490	1.353939	1.310231	1.503158	-1.298140	-1.022768	-0.586283	1.006136	-0.168166	-0.177708	-0.345336	-0.879239	0.405905	-0.287533	-1.159797	-0.292677	-1.646492	-1.906840	-1.695309	-1.604452	0.712311	0.501392	1.133743	0.775186	-1.155892	-0.603892	-0.499700	-0.725896	-0.325474	-0.330597	-0.760112	-0.407714	0.876556	0.865147	-0.152609	0.208927	-1.454865	-0.845984	-1.476690	-1.357216	1.246980	1.024083	1.355200	1.101170	-1.558370	-0.982698	-0.845584	-0.879381	-0.706532	-0.426589
3	-0.085947	0.994871	0.880874	0.178165	-0.220028	-0.040494	-0.509000	1.193483	1.300057	1.232974	2.165211	-0.357505	-0.528676	-0.104386	-0.366438	0.191103	0.471554	-0.881423	-0.764344	-0.946160	-1.050628	0.453216	0.309557	0.604756	0.350035	0.174794	0.178008	0.022001	0.198146	-0.037026	0.010410	1.894026	1.903307	1.437010	1.047931	0.289202	-0.096362	2.771142	2.026416	2.310275	3.607142	0.321949	-0.287000	0.550344	-0.309378	0.416294	0.531538	0.059178	-0.233109	0.001913	0.654431	1.158001	1.488870	1.346832	1.624599	0.423285	-0.074695	0.888511	1.155603	0.701835	0.929060	-0.137530	-0.039736	0.619755	0.620059	0.938153	0.928369	-0.710165	-0.140727	-0.556934	-0.527437	1.246980	0.989130	1.135830	0.874163	0.081161	0.139381	0.760856	0.489119	1.351815	1.760894
4	0.610304	-0.449832	-0.496962	-0.348060	-0.623945	0.782370	-0.104449	0.124399	0.084365	-0.233496	0.525447	0.466249	0.987577	0.355805	0.901630	0.654406	-0.385210	0.642945	1.189374	0.631423	1.012400	-0.402995	-1.050624	-0.498922	-1.029246	0.664978	0.165369	0.469697	-0.033529	0.312752	0.593274	-0.398712	-0.723515	-0.639113	-0.768196	0.689631	-0.157669	0.061310	-0.550963	-0.119138	0.144395	-0.466674	0.575393	-1.039933	0.760173	0.141047	0.002275	0.344025	0.775774	0.409682	-0.056957	-0.643083	-0.703573	-0.599412	-0.691740	0.744057	0.249318	-0.406257	-0.564118	-0.488051	-0.423831	0.617489	-0.449686	-0.456650	-0.662050	0.324869	-0.723837	0.936842	-0.126728	0.832084	0.654358	-0.954497	-0.752523	-0.846379	-0.710930	0.755916	0.043490	-0.845584	-0.350638	-0.912366	-0.528867
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
14196	-1.478448	-2.091198	-1.405825	-1.473700	-0.890096	-1.308487	-1.008158	-2.072790	-0.990327	-2.153611	-2.016117	-1.288085	-1.606864	-1.089361	-1.645938	-1.616962	-0.719503	-1.337860	-1.920332	-1.239441	-1.144996	-1.313963	-0.205049	-0.615774	0.201672	-1.555417	-1.099764	-1.679246	-1.105528	-1.672889	-1.555305	-1.366573	-0.914751	-0.346034	-0.213409	-1.179536	-0.768830	-1.883625	-0.820178	-1.757000	-1.770687	-1.954035	-2.033114	-1.592309	-1.921991	-2.716123	-2.339647	-1.336060	-1.168802	-1.275729	-1.160035	-0.401912	-0.273702	-0.043013	-0.016875	-1.087329	-0.725110	-0.947509	-0.466210	-0.854606	-0.938450	2.793794	2.706535	4.824045	4.316540	-0.161787	0.248206	-1.114070	0.342511	-1.027166	-0.938961	-0.667347	-0.464910	-0.578210	-0.429188	-1.593956	-1.156052	-0.845584	-0.494971	-0.706532	-0.414039
14197	-0.085947	1.903616	1.372148	2.064753	1.480745	0.435372	0.756799	-0.254412	-0.788127	0.253313	0.067979	0.013241	-1.036647	0.346485	-0.962671	0.201414	1.121049	-1.194131	-1.488689	-1.082748	-1.097738	1.411475	1.932397	1.896733	1.933117	0.307522	0.256277	-1.768785	0.027805	-1.900108	-1.779003	3.372158	2.251928	2.950196	2.132921	0.668801	1.619696	1.285060	-0.717822	1.728166	1.340837	1.917123	0.387897	2.231033	0.799781	0.671622	2.083594	0.214394	-1.588728	0.206587	0.048378	1.158001	1.102667	1.640390	1.431090	0.718784	0.708971	-0.250916	0.258035	-0.299589	-0.292305	0.355348	0.401716	1.904362	1.565527	1.758071	2.039649	-0.981539	-0.438252	-0.958567	-0.852944	2.443435	2.072669	2.560108	2.168658	0.218172	0.567258	-0.845584	0.017576	-0.844415	-0.426589
14198	0.610304	0.266109	-0.481102	0.066117	-0.591381	0.693471	1.045651	0.748462	-0.695092	0.524779	0.562239	-0.313861	0.891498	-0.539369	0.833799	0.621797	0.049092	0.767899	0.870994	0.735292	0.921399	0.970925	-0.666493	0.422465	-0.846406	0.623916	0.905770	0.977086	-0.689169	0.970904	1.048230	-0.623851	-0.657809	-0.674376	-0.763186	0.598599	0.249896	0.061310	-0.333918	-0.183294	0.262059	-0.351612	0.528553	-0.535126	0.452080	0.480154	0.131815	0.258230	0.559363	0.274346	0.175929	-0.606537	-0.617177	-0.575859	-0.668568	0.778857	0.532942	-0.406257	-0.463980	-0.487880	-0.315716	0.223187	0.413732	-0.518312	-0.645890	-0.150049	-0.746049	0.936842	0.738181	0.869623	1.103826	-0.954497	-0.902438	-0.846379	-0.842973	0.755916	0.613314	-0.845584	-0.498991	-0.912366	-0.894414
14199	-0.085947	0.164755	-0.362519	-0.104229	-0.590119	0.012663	-0.174827	0.333730	0.124290	0.544126	0.835220	0.166624	0.982838	-0.088200	0.892621	0.026302	-0.432043	0.646183	1.141963	0.915079	1.018390	-0.193920	-0.685790	-0.547400	-0.912746	-0.005710	-0.091954	0.753238	0.224088	0.783566	1.191428	-0.126463	-0.589818	-0.690544	-0.767177	0.053108	-0.112398	0.061310	-0.401759	-0.005779	0.362177	0.520332	0.634797	0.949178	0.992737	0.620498	0.170659	-0.508810	0.737250	-0.381553	-0.228306	-0.657693	-0.666565	-0.661538	-0.685960	-0.047294	-0.029471	-0.406257	-0.539122	-0.422124	-0.372554	0.420372	-0.458102	-0.690902	-0.662523	-1.440428	-0.932149	0.936842	-0.117210	1.175651	0.663767	-0.428057	-0.710579	-0.403610	-0.677101	0.112926	0.107950	-0.042364	-0.436394	-0.029014	-0.379847
14200	-1.478448	0.460167	0.993853	0.855996	1.212113	-1.398881	-1.176656	-1.159008	0.487224	-0.907551	-0.791195	1.572205	0.204162	2.154177	0.553964	-1.599816	-0.747818	-1.606219	-1.512602	-1.617288	-1.463344	-1.961099	-0.532680	-1.179136	-0.045297	-1.543243	-1.157021	-1.947864	-0.661705	-2.067511	-1.905235	-0.044777	0.233861	0.683581	0.731609	-1.113070	-0.604060	-1.992831	-0.602926	-1.890743	-1.906671	2.116406	1.672274	2.372663	1.964612	-1.370022	-0.881358	-0.147208	0.838452	0.331127	0.515563	0.747966	0.554957	1.184261	0.839474	-1.141669	-0.604862	-0.539505	-0.678272	-0.372508	-0.376533	-1.642104	-1.314825	-0.514486	-0.448631	-1.561900	-0.805520	-1.290778	-1.017752	-1.260253	-1.154844	2.204144	2.051697	2.315947	2.146972	-1.553146	-1.064936	-0.845584	0.120085	-0.706532	-0.414039

Prospecção de Dados 2021/2022¶

Second Home Assignment - Best Features and Model Selection¶

Group 4¶

0.1 - Import Libraries¶

0.2 - Import Dataset¶

0.3 - Exploratory Data Analysis¶

0.3.1 - Profile Report¶

0.3.2 - Inspecting Data types and missing values¶

0.3.3 - Cheking and dropping duplicates¶

0.3.4 - Inferring Outliers¶

0.4 - Data Partition¶

0.5 - Data Standardization¶

0.6 - Inferring the variance of attributes¶

0.7 - Defining Functions¶

1- Selecting the Best Features and Dimensionality Reduction¶

1.1 - Pearson Correlation¶

1.2 - Select From Model¶

1.2.1 - Random Forest Regressor¶

1.2.2 - Decision Tree Regressor¶

1.2.3 - Linear Regression¶

1.3 - Sequential Feature Selector¶

1.4 - Best Features Selected¶

2 - Principal Components Analysis¶

3 - Finding the best model¶

3.1 - Feature Selection Method set¶

3.1.1 - Format the Final Results dataset¶

3.2 - Principal Components set¶

3.2.1 - Format the Final Results dataset¶

4 - Training the Best Model¶

4.1 - Feature Selection Method set¶

4.1 - Principal Components set¶

	count	propotion
std_FusionHeat	1115.0	0.052602
range_FusionHeat	1050.0	0.049535
wtd_std_FusionHeat	887.0	0.041846
range_ElectronAffinity	639.0	0.030146
wtd_mean_atomic_mass	537.0	0.025334
...	...	...
std_atomic_radius	0.0	0.000000
entropy_ThermalConductivity	0.0	0.000000
std_fie	0.0	0.000000
wtd_std_fie	0.0	0.000000
range_ThermalConductivity	0.0	0.000000

	number_of_elements	mean_atomic_mass	wtd_mean_atomic_mass	gmean_atomic_mass	wtd_gmean_atomic_mass	entropy_atomic_mass	wtd_entropy_atomic_mass	range_atomic_mass	wtd_range_atomic_mass	std_atomic_mass	wtd_std_atomic_mass	mean_fie	wtd_mean_fie	gmean_fie	wtd_gmean_fie	entropy_fie	wtd_entropy_fie	range_fie	wtd_range_fie	std_fie	wtd_std_fie	mean_atomic_radius	wtd_mean_atomic_radius	gmean_atomic_radius	wtd_gmean_atomic_radius	entropy_atomic_radius	wtd_entropy_atomic_radius	range_atomic_radius	wtd_range_atomic_radius	std_atomic_radius	wtd_std_atomic_radius	mean_Density	wtd_mean_Density	gmean_Density	wtd_gmean_Density	entropy_Density	wtd_entropy_Density	range_Density	wtd_range_Density	std_Density	wtd_std_Density	mean_ElectronAffinity	wtd_mean_ElectronAffinity	gmean_ElectronAffinity	wtd_gmean_ElectronAffinity	entropy_ElectronAffinity	wtd_entropy_ElectronAffinity	range_ElectronAffinity	wtd_range_ElectronAffinity	std_ElectronAffinity	wtd_std_ElectronAffinity	mean_FusionHeat	wtd_mean_FusionHeat	gmean_FusionHeat	wtd_gmean_FusionHeat	entropy_FusionHeat	wtd_entropy_FusionHeat	range_FusionHeat	wtd_range_FusionHeat	std_FusionHeat	wtd_std_FusionHeat	mean_ThermalConductivity	wtd_mean_ThermalConductivity	gmean_ThermalConductivity	wtd_gmean_ThermalConductivity	entropy_ThermalConductivity	wtd_entropy_ThermalConductivity	range_ThermalConductivity	wtd_range_ThermalConductivity	std_ThermalConductivity	wtd_std_ThermalConductivity	mean_Valence	wtd_mean_Valence	gmean_Valence	wtd_gmean_Valence	entropy_Valence	wtd_entropy_Valence	range_Valence	wtd_range_Valence	std_Valence	wtd_std_Valence
0	1.306555	0.334165	-0.419664	-0.014535	-0.626718	1.008033	1.083041	1.405015	-0.321791	1.227995	1.181915	-0.250489	0.992170	-0.320051	1.004719	1.146015	0.322742	0.617372	0.974192	0.417869	0.834902	0.196021	-1.042166	0.040596	-0.993816	1.174148	1.374300	0.514467	-0.830453	0.361047	0.524424	-0.258936	-0.704816	-0.580864	-0.766137	1.033259	1.162524	0.260752	-0.673723	0.374641	0.440543	-0.267787	0.434649	-0.645118	-0.039040	1.033708	0.268355	0.303600	0.614585	0.199037	0.341818	-0.411390	-0.619442	-0.429184	-0.671899	1.321201	1.682306	-0.222157	-0.586911	-0.369920	-0.313067	0.524079	-0.178020	-0.442188	-0.654768	0.738500	0.818370	0.936842	-0.226341	0.789459	0.650119	-0.507820	-0.624658	-0.536731	-0.668001	1.069458	0.967296	0.760856	-0.460712	0.539883	0.724916
1	0.610304	0.140465	-0.410864	0.016523	-0.603968	0.740366	0.234766	0.333730	0.001998	0.253318	0.751189	-0.219946	0.996772	-0.403260	0.919825	0.633091	-0.274733	0.646183	1.141963	0.683308	0.999207	0.383524	-0.709740	0.047412	-0.920298	0.646600	0.321668	0.753238	0.042812	0.645321	1.154730	-0.216270	-0.613330	-0.598906	-0.767364	0.831456	0.324563	0.061310	-0.481658	-0.195611	0.330969	0.085694	0.618124	0.451715	0.949392	1.130012	0.244078	-0.160853	0.747095	-0.244510	-0.181220	-0.576230	-0.661128	-0.569157	-0.685294	0.723624	0.505562	-0.406257	-0.559308	-0.435302	-0.360814	-0.041411	-0.455782	-0.650204	-0.662415	-0.971017	-0.848555	0.936842	-0.117210	0.945724	0.663216	-0.380198	-0.710579	-0.336916	-0.677101	0.704719	0.402872	-0.042364	-0.429805	-0.195379	-0.379847
2	-0.782197	0.252380	-0.414731	-0.262988	-0.753002	-0.994672	-0.866623	0.945576	0.244512	1.211634	1.480720	0.668856	1.900437	0.042562	2.200917	-0.804877	-1.227990	1.090642	1.957835	1.439668	0.440877	0.536182	-1.472135	-0.429557	-1.361974	-0.909165	-0.379473	1.156165	-0.493244	1.692161	0.775233	0.286790	-0.189206	-0.837170	-0.776760	-2.363929	-2.428749	2.564056	0.688110	3.160510	2.990152	0.483661	0.946174	0.949408	1.443471	-0.196763	-0.898839	-0.455934	1.419230	-0.453087	-0.658353	-0.154941	-0.365119	-0.745143	-0.708312	-2.232150	-2.061980	0.683414	0.011281	0.903393	0.991955	-0.357798	-0.844600	-0.686343	-0.670182	-0.488646	-0.968302	-0.514691	-0.500626	-0.476913	-0.384311	-0.188766	-0.205442	-0.731209	-0.456180	-1.145811	-0.772135	2.367297	-0.098634	2.710833	2.308579
3	-0.085947	-1.208293	-0.954077	-0.897135	-0.735068	0.204932	0.360330	-0.812840	-0.690344	-0.892239	-0.662078	0.332860	0.939266	0.156511	0.938359	0.046307	-0.104955	0.617372	0.791414	0.816914	0.836115	-0.318369	-0.922682	-0.600846	-0.927253	0.014234	0.395911	0.469697	-0.668986	0.603469	0.608187	-0.992152	-0.747910	-0.802060	-0.764569	-0.692639	-0.983812	0.061310	-0.231268	-0.013955	0.266862	-0.314677	0.465204	-0.990316	-0.100781	-0.652230	-0.370461	0.303600	0.543982	0.672861	0.442594	-0.601090	-0.601701	-0.627829	-0.665300	0.036204	-0.004411	-0.406257	-0.431119	-0.428064	-0.293115	1.788756	0.869919	-0.389017	-0.636564	0.267181	-0.202885	0.936842	0.996020	0.986334	1.194279	-1.145929	-0.968232	-1.007869	-0.897970	0.225633	0.212247	-1.648805	-0.548924	-1.735705	-1.478668
4	2.002805	0.743780	-0.415774	0.304921	-0.612102	1.494279	1.283314	1.405015	-0.361580	1.393472	1.124376	-0.397983	0.952036	-0.447934	0.949174	1.560259	0.387796	0.674022	0.974541	0.297841	0.850626	0.026533	-0.991195	0.025287	-0.964609	1.624071	1.297820	0.469697	-0.638515	0.068897	0.556933	-0.075529	-0.708748	-0.472704	-0.765361	1.619203	1.411190	0.640177	-0.710517	0.419463	0.432758	-0.437313	0.362343	-0.640622	-0.154960	1.517544	0.231955	0.303600	0.589501	0.078131	0.441133	-0.596334	-0.633996	-0.508691	-0.672198	1.786567	1.516328	-0.406257	-0.574177	-0.517153	-0.350558	0.246124	-0.197825	-0.385199	-0.653220	1.199891	0.860676	0.936842	-0.207711	0.650248	0.642817	-0.325503	-0.649540	-0.370203	-0.685290	1.469934	1.097855	0.760856	-0.426768	0.579644	0.644082
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
6991	-0.085947	0.061498	-0.532575	-0.150423	-0.595028	0.035731	0.655114	0.160989	-0.792751	0.394075	0.343387	0.020668	0.835052	-0.312512	0.741530	0.005902	-0.112150	0.767899	0.733299	1.006991	0.963271	0.764339	-0.591339	0.002933	-0.813894	-0.059769	0.522653	0.977086	-0.922599	1.422283	1.155525	-0.468104	-0.607611	-0.731527	-0.761593	-0.113909	-0.098222	0.061310	-0.252999	-0.036973	0.312244	0.195255	0.574459	0.216005	0.592603	0.265883	0.158596	0.106084	0.451375	0.101774	0.088750	-0.637637	-0.609336	-0.647168	-0.665574	0.002405	0.033938	-0.406257	-0.437982	-0.432872	-0.304761	0.465769	0.544809	-0.666859	-0.645587	-1.284537	-1.170704	0.936842	0.941431	1.159755	1.203039	-0.667347	-0.844914	-0.646150	-0.809008	0.087584	0.481187	-0.042364	-0.750774	0.046876	-0.344453
6992	-0.085947	-0.617192	-0.094680	-0.099492	0.280370	0.555737	0.299680	-1.541017	-0.215174	-1.582173	-1.471937	-0.192983	-0.552077	0.020663	-0.469466	0.175752	0.575817	-0.570334	-0.603660	-0.688036	-0.603593	0.117203	0.590803	0.529010	0.732829	0.237862	0.213186	-0.515235	-0.045333	-0.613016	-0.553056	0.060296	0.225919	0.608461	0.622740	0.674715	0.781207	-0.592607	-0.192349	-0.613979	-0.839665	-1.255820	-1.569777	-0.921945	-1.410496	0.022258	0.010758	-0.816342	-1.004712	-0.831094	-0.586385	0.197540	0.322240	0.479969	0.489563	0.529323	0.205505	-0.066817	0.204667	-0.130314	0.043557	-0.617437	-0.487865	0.917556	0.721509	1.786969	1.932624	-1.177180	-0.880023	-1.231797	-1.218332	0.289816	0.408856	0.244098	0.322656	0.091556	0.046922	0.760856	0.359547	0.565597	1.120013
6993	1.306555	0.221467	-0.498930	0.002771	-0.604308	1.148019	0.957241	0.642559	-0.456149	0.611064	0.525387	-0.689977	0.906421	-0.893205	0.830230	1.109055	-0.053008	0.767899	0.990568	0.589834	0.956655	1.374140	-0.657620	0.868554	-0.860705	1.148542	0.780544	0.977086	-0.374174	0.866348	1.133108	-0.406056	-0.629291	-0.588157	-0.764143	1.144053	0.452432	0.087092	-0.350593	0.048607	0.360545	-0.461841	0.550801	-0.587935	0.524292	1.087995	0.149042	0.303600	0.611085	0.093429	0.151003	-0.424761	-0.574484	-0.455944	-0.666608	1.202709	0.704349	-0.067911	-0.461696	-0.264865	-0.176636	0.463550	0.334237	-0.463585	-0.650621	0.606196	-0.938408	0.936842	0.696304	0.810073	1.104396	-0.667347	-0.894024	-0.623725	-0.839007	1.150822	0.615173	-0.042364	-0.424003	-0.163617	-0.753321
6994	-0.782197	0.627589	0.799582	1.026894	1.054208	-0.269704	0.035524	-0.981248	-0.672325	-0.950510	-0.912460	-0.220022	-0.492548	-0.155517	-0.436228	-0.616626	0.152864	-0.419807	-0.910897	-0.283269	-0.489657	1.033979	1.014855	1.145933	0.996134	-0.594746	-0.123059	-0.007846	-0.840387	0.241325	-0.059039	0.342568	0.779571	0.751370	0.971681	-0.293036	0.054424	-0.047062	0.488270	0.104652	0.126571	-0.969338	-1.106303	-0.469704	-0.721490	-0.393850	0.269618	-0.968488	-1.067076	-1.038243	-1.031875	0.290392	0.397455	0.534420	0.580490	-0.285166	-0.063798	-0.066817	0.121452	-0.024370	-0.024431	-1.127609	-0.651915	0.300481	0.484590	0.758254	1.069828	-1.252912	-0.865070	-1.288690	-1.211558	0.449344	0.709507	0.349437	0.640080	-0.667463	-0.295153	0.760856	0.120085	0.831505	0.901914
6995	-1.478448	2.157957	2.334858	2.251598	2.243125	-1.494333	-1.101658	-0.088798	0.819696	0.551820	0.699613	-0.799659	-1.195420	-0.484080	-1.115857	-1.598059	-0.710573	-1.757717	-2.081606	-1.830596	-1.640655	0.702114	1.300661	1.214275	1.403447	-1.555970	-1.101096	-1.544937	-0.955666	-1.475577	-1.365909	1.649909	1.708441	1.985267	1.928031	-1.113898	-0.516388	-1.859789	-0.982501	-1.727809	-1.734386	-0.790794	-1.167225	-0.089656	-0.648458	-1.278866	-0.483363	-1.433283	-1.427487	-1.407136	-1.278821	0.550526	0.470175	0.299893	0.232409	-1.959915	-1.503576	0.506877	0.672723	0.863897	1.108709	-0.072678	0.116358	1.175359	1.050983	-0.691297	-0.124700	-0.931051	-0.235832	-0.785755	-0.698833	1.725562	1.548376	1.763212	1.569111	-1.593956	-1.008824	-0.042364	-0.494971	0.322642	0.694496

	critical_temp
wtd_std_ThermalConductivity	0.720960
range_ThermalConductivity	0.687282
range_atomic_radius	0.653394
std_ThermalConductivity	0.653232
wtd_entropy_atomic_mass	0.626536
wtd_entropy_atomic_radius	0.602986
number_of_elements	0.600394
range_fie	0.600179
wtd_std_atomic_radius	0.598972
entropy_Valence	0.598024
wtd_entropy_Valence	0.589204
wtd_std_fie	0.581442
entropy_fie	0.567156
wtd_entropy_FusionHeat	0.562808
std_atomic_radius	0.559132
entropy_atomic_radius	0.558249
entropy_FusionHeat	0.552069
entropy_atomic_mass	0.542894
std_fie	0.541091

	PC1	PC2	PC3	PC4
0	5.414926	-2.041308	-2.633267	7.741479
1	-4.679600	-0.326168	2.389260	0.412023
2	7.903280	0.968208	0.413308	0.031600
3	2.493496	-2.655079	-6.081691	2.035512
4	-4.165676	0.817865	2.233788	0.452753
...	...	...	...	...
14196	5.951361	2.782436	4.341706	-6.968918
14197	5.586579	-6.029637	-5.473172	1.703294
14198	-5.030727	-0.618209	2.444568	0.144282
14199	-3.227114	1.178488	2.349165	2.204764
14200	7.206284	3.795183	0.161777	4.266506

	PC1	PC2	PC3	PC4
0	-5.857828	-1.562840	-0.668722	-0.007666
1	-4.177553	-0.130448	1.924870	1.226300
2	-1.292051	4.083983	-0.614974	5.548708
3	-3.686521	2.174282	3.576733	-0.494505
4	-6.298011	-2.586264	-1.067430	-0.212216
...	...	...	...	...
6991	-4.067375	0.814397	2.607586	1.243962
6992	2.636201	-1.326014	-1.879953	-4.138144
6993	-5.405420	-1.481888	1.594204	-0.267734
6994	3.916529	-1.670146	-1.234818	-1.505546
6995	9.412228	-1.951766	0.041344	-0.458290

	Algorithm	params	mean_test_score
1265	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 5, 'n_estimators': 1000, 'random_state': 42}	0.899196
1259	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 3, 'n_estimators': 1000, 'random_state': 42}	0.899122
1262	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 4, 'n_estimators': 1000, 'random_state': 42}	0.898333
1256	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 2, 'n_estimators': 1000, 'random_state': 42}	0.897450
1185	Ada Boost with Decision Tree Regressor	{'learning_rate': 0.2, 'loss': 'square', 'n_estimators': 100, 'random_state': 42}	0.896907
1258	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 3, 'n_estimators': 500, 'random_state': 42}	0.896711
1264	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 5, 'n_estimators': 500, 'random_state': 42}	0.896620
1261	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 4, 'n_estimators': 500, 'random_state': 42}	0.895696
1255	Gradient Boosting Regressor	{'max_depth': 5, 'min_samples_split': 2, 'n_estimators': 500, 'random_state': 42}	0.894743
1188	Ada Boost with Decision Tree Regressor	{'learning_rate': 0.2, 'loss': 'exponential', 'n_estimators': 100, 'random_state': 42}	0.894579

	Algorithm	params	mean_test_score
1185	Ada Boost with Decision Tree Regression	{'learning_rate': 0.2, 'loss': 'square', 'n_estimators': 100, 'random_state': 42}	0.852275
1197	Ada Boost with Decision Tree Regression	{'learning_rate': 0.5, 'loss': 'exponential', 'n_estimators': 100, 'random_state': 42}	0.852186
1188	Ada Boost with Decision Tree Regression	{'learning_rate': 0.2, 'loss': 'exponential', 'n_estimators': 100, 'random_state': 42}	0.851817
1191	Ada Boost with Decision Tree Regression	{'learning_rate': 0.5, 'loss': 'linear', 'n_estimators': 100, 'random_state': 42}	0.850573
1183	Ada Boost with Decision Tree Regression	{'learning_rate': 0.2, 'loss': 'linear', 'n_estimators': 500, 'random_state': 42}	0.850042
1194	Ada Boost with Decision Tree Regression	{'learning_rate': 0.5, 'loss': 'square', 'n_estimators': 100, 'random_state': 42}	0.849272
1182	Ada Boost with Decision Tree Regression	{'learning_rate': 0.2, 'loss': 'linear', 'n_estimators': 100, 'random_state': 42}	0.848505
1206	Ada Boost with Decision Tree Regression	{'learning_rate': 0.8, 'loss': 'exponential', 'n_estimators': 100, 'random_state': 42}	0.847830
1189	Ada Boost with Decision Tree Regression	{'learning_rate': 0.2, 'loss': 'exponential', 'n_estimators': 500, 'random_state': 42}	0.846767
1200	Ada Boost with Decision Tree Regression	{'learning_rate': 0.8, 'loss': 'linear', 'n_estimators': 100, 'random_state': 42}	0.843199